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A computationally efficient method to study the in-plane and out-of-plane dimensional instability of thin paper sheets under the influence of moisture changes is presented. The method explicitly resolves the bonded and the free segments of fibers in the sheet, capturing the effect of anisotropic hygroexpansion at the fiber level. The method is verified against a volumetric model. The importance of longitudinal fiber hygroexpansion is demonstrated in spite of the absolute value of longitudinal hygroexpansion being an order of magnitude lower than the transverse hygroexpansion component. Finally, the method is used to demonstrate the formation of macroscopic sheet curl due to a moisture gradient in structurally uniform sheets in the absence of viscoelastic or plastic constitutive behavior and through-thickness residual stress profiles. [ABSTRACT FROM AUTHOR]

Abstract: Continuum damage mechanics (CDM) is used to describe the post-elastic behavior of low-basis-weight paper. The relevance of undertaking studies of the mechanical behavior of low-basis-weight paper is that it enables characterization, optimization and quality control. In accordance with a CDM theory, an internal variable is introduced that represent the degree to which the material has degraded in a continuum sense and details inherent in a damage evolution law contain information about the rupture mechanism. To account for long ranging micro-structural effects, because of the fiber structure in the paper material, a non-local formulation of the constitutive law is considered. Of particular interest is the fracture toughness of the material, i.e. the ability to resist further crack propagation, as it is often a good measure of flaw tolerance and durability in the context of paper. The constitutive model discussed is verified against tensile tests on rectangular paper specimens containing pre-fabricated cracks. Acoustic emission was used to study the damage evolution in paper specimens during tensile loading. An orthotropic material description has been utilized. The model is contrasted with a purely isotropic formulation. It seems that for the type of problem analyzed in this work, an orthotropic material description does not significantly improve the predictive capability as compared to an isotropic formulation. It is concluded that the model can be used to evaluate the influence of arbitrary defect geometries, defect size and loading conditions and can easily be incorporated into a finite element code. [Copyright &y& Elsevier]

The mechanical behavior of two packaging paper materials subjected to tensile loading up to complete breakage has been investigated. A model for isotropic strain hardening elastic anisotropic plasticity, coupled to anisotropic damage, is discussed. The constitutive relations, including a gradient enhanced damage model, are developed within a thermodynamical framework. The Helmholtz free energy in the continuum is assumed to depend not only on the strain and stress components but also on the damage in the material.The model has been analyzed in a non-linear finite element procedure. The capability of the model to properly capture and simulate the failure of a paper material subjected to tensile loading is demonstrated by means of several numerical examples that are compared to, and verified with, experiments on packaging paper specimens of varying geometry. [Copyright &y& Elsevier]

In fibrous paper materials, an exposure to a variation in moisture content causes changes in the geometrical and mechanical properties. Such changes are strongly affected by the inter-fibre bonds, which are responsible for the transfer of the hygro-mechanical response from one fibre to its neighbours in the network, resulting in sheet-scale deformation. Most models developed in literature assume perfect bonding between fibres. In the 3D reality, there is some flexibility in the bond region, even for the perfectly bonded fibres, because of the possibility of deformation gradients through the fibre thickness. In earlier 2D idealizations, perfectly bonded fibres were assumed, implying full kinematic constraint through the entire thickness of the sheet. The purpose of the present study is to assess the effect of this assumption. Using a homogenization approach, a random network of fibres is generated with different coverages and modelled using finite elements. In order to understand the role of bonding between fibres on the hygro-expansive behaviour of a network, a bond model is developed. In this model, the fibres are modelled using 2D regular bulk finite elements and the bonds are represented by interfacial elements of finite stiffness, which are introduced between each pair of fibres bonded in the network. These embedded interfacial elements form a connection between two respective fibres, allowing relative displacements between their mid-planes. The hygro-elastic response of networks obtained with this bond model is investigated by varying the bond stiffness and the network coverage under the application of mechanical loading and changes in moisture content. Furthermore, the bond model is used to analyse the influence of inter-fibre bonds on the anisotropic response of the paper fibre network. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a method to predict the through-thickness moisture content distribution and associated induced deformations of paper and cardboard sheets as they are subjected to relative humidity changes. The transient moisture diffusion problem is solved using a “natural” analytic approach that has previously been applied for solving transient heat conduction in multi-layer solids. The deformation behaviour of the sheet during the moisture diffusion process is predicted using a semi-analytical approach based on a Rayleigh–Ritz minimization of the total potential energy. Geometrically nonlinear effects are taken into account. Curvatures of the originally flat sheet are predicted as a function of time, as are the shapes of the sheet for steady-state condition. As multiple solutions exist, stability is studied. The developed model was used to study the deformation behaviour of one paper and two cardboard sheets. Comparisons with finite-element results demonstrate that the developed model provides accurate results. The displacements obtained for steady-state conditions are within +6%. Comparisons with previous steady-state analyses reveal important differences in the shape of one cardboard sheet. This suggests that the moisture diffusion process may influence the configuration assumed by the sheet at steady-state equilibrium. Hence, it may be necessary to take the moisture diffusion into account in the analysis to accurately predict the hygro-mechanical behaviour of paper or cardboard sheets. [Copyright &y& Elsevier]

Abstract: An anisotropic elasto-plastic constitutive model of paper material is presented. It is formulated in a spatial setting in which anisotropic properties are accounted for by use of structural variables. A multiplicative split of the deformation gradient is employed to introduce plasticity. A similar approach is used to model the plastic deformation of the substructure. The yield surface adopted is based on the Tsai–Wu failure criterion, used previously to model failure of paper material. A non-associated plasticity theory is employed to calibrate the model to experimental data. It turns out that a multi-axial loading situation is needed to calibrate the model and here a biaxial tension test is audited. The model was implemented into a finite element environment and the creasing process of a corrugated board panel is investigated. [Copyright &y& Elsevier]

Abstract: Strains, computed by the finite element method, are evaluated and compared to an experimentally determined strain field. The analyzed low-density paper has been designed to ensure bond–breakage as the dominating damage mechanism and the paper material is approximately in-plane isotropic. An optical non-contact displacement measuring system has been used in fracture tests to determine the strain field in the crack-tip region of a pre-fabricated crack. Additionally, acoustic emission monitored tensile tests have been conducted to determine onset and evolution of damage processes and thereby enabling calibration of required constitutive parameters. The results suggest that the investigated paper material can tolerate significantly higher strains than what is predicted by a classic elastic–plastic J 2-flow theory. Immediately before onset of the final fracture (i.e., localization), the experimental measured normal strain in the near-tip region is around 60% higher than the computed strain when using exclusively an elastic–plastic theory for the corresponding load while the strain computed utilizing a non-local damage theory is of the same order of magnitude as the experimentally measured strain. Hence, it seems essential to include a non-local continuum theory to describe strains in the near-tip region quantitatively correct for paper materials. It is demonstrated that path independence of the well-known J-integral does not prevail for this class of material models. Only for the special situation of a homogenous damage field in the crack-tip region may the stress and strain fields be described by the well-known HRR-solutions. [Copyright &y& Elsevier]

Abstract: The creep of paper is accelerated by moisture cycling. This effect is known as mechano-sorptive creep. It is assumed that this is an effect of transient stresses produced during moisture content changes in combination with non-linear creep behaviour of the fibres. The stresses produced by the moisture content changes are often much larger than the applied mechanical loads. If this is the case, the mechanical loads are only a perturbation to the internal stress state, and it will appear as if the mechano-sorptive creep is linear in stress. It is possible to take advantage of this feature. In the present report the pure moisture problem is first solved. The mechanical load is then treated as a perturbation of the solution to the moisture problem. Using this strategy, it is possible to linearize a non-linear network model for mechano-sorptive creep and to formulate a continuum model. As a result, the number of variables in the model is reduced. This is a significant improvement as it will be possible to use the linearized model to describe the material in a finite element program and solve problems with complicated geometries. [Copyright &y& Elsevier]

Paper is a complex material consisting of a network of cellulose fibres at the micro-level. During manufacturing, the network is dried under restraint conditions due to tension in the paper web in machine direction. This gives rise to internal strains that are stored in the produced sheet. Upon exposure to a moisture cycle, these strains may be released. This results in permanent shrinkage that may cause instabilities such as curl or waviness of the sheet. The prime objective of this paper is to model this irreversible shrinkage and to link its magnitude to the properties of the fibres and of the network. For this purpose, randomly generated fibrous networks of different coverages (i.e. ratio of the area occupied by fibres and that of the sheet) are modeled by means of a periodic representative volume element (RVE). Within such RVEs, a finite element method combined with a kinematic hardening plasticity model at the scale of the fibres is used to capture the irreversible response. The computational results obtained demonstrate that the magnitude of the irreversible strains increases with coverage until a certain coverage and beyond that coverage decreases in magnitude. This phenomenon is explained by considering the area fraction of free-standing fibre segments relative to bonded fibre segments in the network. A structure–property dependency of irreversible strains at the sheet-level on the micro-structural parameters of the network is thereby established. [ABSTRACT FROM AUTHOR]

This paper addresses the propagation of coupled axial-flexural waves in metamaterial beams with rod-like resonators. Utilizing an exact frequency-dependent stiffness method, based on Euler–Bernoulli beam assumption for rods and host beam, and fully accounting for axial-flexural coupling phenomena, several adimensional parametric analyses are performed for investigating the dispersive properties of the metamaterial beams. The analyses reveal novel and relevant aspects unaddressed in previous studies. Firstly, they show that certain rod configurations lead to significant interference between flexural resonance and the band gaps opened by axial resonance, whereas other configurations enable flexural resonance to open substantial band gaps without interference from axial resonance. Results are complemented by 3D finite element analyses proving evidence of the findings and validating the method. Additional analyses demonstrate that adding a tip mass to the rods, while keeping the total mass of the resonator unchanged, can significantly reduce the opening frequency of the band gaps and can attenuate or remove the interference caused by flexural resonance within the band gaps opened by axial resonance; the rotational inertia of the tip mass can also play a significant role in removing flexural resonance interference. Notably, the paper also reveals that the attenuation phenomena for the coupled problem with a single set of rods are governed by the opening of weak band gaps, rather than by traditional band gaps; this aspect is elucidated by showing Bloch mode shapes of the infinite metamaterial beam and frequency response of the corresponding finite beam. Results and proposed design prove to be useful and promising for locally resonant beams featuring rod-like resonators, both as an alternative to traditional beam-like resonators and for their applicability in the 3D printing process of locally resonant structures, where rods serve as elastic elements in constructing the resonators. • Dispersive properties of metamaterial beams with rod-like resonators are addressed by an exact approach based on frequency-dependent stiffness concept. • Certain rods configurations cause flexural resonance to significantly interfere with the band gaps opened by axial resonance. • Other rods configurations enable flexural resonance to open band gaps of significant width without interference from axial resonance. • Tip mass on the rods and its rotational inertia can remove the interferences caused by flexural resonance and lower the band gaps opening frequency. • Dispersive properties of the coupled problem with a single set of rods are primarily determined by the weak band gaps opening. [ABSTRACT FROM AUTHOR]

• Studied dynamic loading behavior of keratin-based horn material. • Developed a novel numerical model to account for anisotropic features and strain-rate effects. • Model validated with uniaxial compression tests under quasi-static and dynamic conditions. • Detailed analysis of energy absorption, stress distribution, and displacement wave propagation. The horn of the bighorn sheep is composed of keratin-based biological material that has a tubule-lamella structure, which gives it anisotropic hardening properties under impact loading. This paper aims to investigate the energy dissipation mechanisms inherent in bighorn sheep horns by developing a numerical material model that accounts for the horn's anisotropic features and strain-rate effects. To this end, a transversely isotropic constitutive model, which includes both anisotropic hardening and strain-rate effects, was formulated to accurately predict the mechanical behavior of bighorn sheep horns. Material characterization was conducted through uniaxial compression tests that were conducted under quasi-static and dynamic conditions. The developed constitutive model was implemented into LS-Dyna via a user-defined material subroutine and was validated against empirical data. The validated numerical model was used to investigate the horn's mechanical responses under dynamic loading conditions. The paper focused on impact energy dissipation mechanisms, including energy absorption and transition, stress distribution, and displacement wave propagation. The insights gained from this paper are expected to significantly contribute to the development of novel artificial materials with enhanced energy absorption and impact mitigation properties. [ABSTRACT FROM AUTHOR]

• Introduction of a novel homogenization approach for multi-phase composites. • Accurately captures stresses at both effective and individual inclusion levels. • Extensively validated using finite element analysis (FEA) on virtual and microCT-derived Representative Volume Elements. • Offers predictions comparable to full finite element approaches but at significantly lower computational costs. • Provides improved predictions of micromechanical behaviour using the Modified Coulomb criteria. Mean field homogenization (MFH) methods are widely employed for homogenizing heterogeneous materials. However, they are limited to predicting effective properties and phase-averaged stresses, failing to capture stresses within individual inclusions. This paper introduces a novel homogenization approach, termed MDMT-Voigt, aimed at addressing this lacuna. The proposed model is validated extensively using finite element analysis (FEA), encompassing virtual Representative Volume Elements (RVEs) with a range of aspect ratios, volume fractions, and orientation distributions. Furthermore, validation is conducted using RVEs derived from experimentally determined microstructures via micro-computed tomography. Across all models considered, the FEA results yield a range of stresses for inclusions with same orientation and aspect ratio which is captured well by the proposed MDMT-Voigt model. Prediction of stresses in individual inclusions represents a significant advancement over conventional MFH methods, offering substantial potential for enhanced micromechanics modelling comparable to full finite element approaches, but at a computational efficiency order of magnitude lower. The paper ends with a demonstration confirming improved micromechanics using the Modified Coulomb criteria. [ABSTRACT FROM AUTHOR]

Origami arrays featuring ideal purely rotational creases inherently possess multiple kinematic degrees of freedom. The incorporation of crease rotational stiffness introduces additional constraint relations to the kinematic morphology of the origami array, due to the interaction between the plate and the crease. This paper concentrates on elucidating the coupling effect, employing two theoretical models to systematically analyze the uniform stretch process of single crease origami arrays. The validity of our theoretical approaches is substantiated through verification in the finite element method. Firstly, the mechanical equations of the origami unit, together with the length and angle constraint equations of the origami array, are amalgamated to formulate a comprehensive set of morphological computational equations specific to the single crease origami array. This set enables the realization of morphological analysis for general origami arrays. Moreover, energy equations for the origami array are computed using an equivalent rigid plate nonlinear creasing element. When combined with constraint equations corresponding to horizontal stretch displacement, these energy equations contribute to the establishment of a nonlinear optimization framework for determining the morphology of uniform single crease origami arrays. Notably, our investigation reveals that during the early stages of the unfolding process for a single crease origami array, even a small relative horizontal stretch displacement can induce a drastic change in the center crease. Through finite element analysis of general origami arrays, it is shown that the proposed theoretical analysis method applies to different crease stiffness, both unfolding and folding processes, and different plate types. The research method in this paper can provide ideas for systematically analyzing the influence mechanism of crease properties on the morphological features of origami structures. • Mechanical equations of origami arrays are established for morphological analysis. • Optimization framework is developed using equivalent crease for origami arrays. • Theoretical approaches are verified by numerical simulation and experiments. • A small horizontal edge stretch can induce a drastic change in the center crease. [ABSTRACT FROM AUTHOR]

• The non-uniform wrapping process is studied in theoretical analysis, numerical simulation and experiments. • A tape spring can be rolled around a hub, and localized folds are formed. • A theoretical model is presented to predict the shape of the tape spring during the non-uniform wrapping process. • The shape of a tape spring after non-uniform wrapped is a polygon or a continuous curve. • The shapes of four tape springs stay the same as that of single tape spring. A tape spring, which has a high ratio of retraction and deployment, is a type of basic deployable member that plays an important role in deployable structures. This paper is focused on the non-uniform wrapping process of a tape spring that the fixed end section preserves the initial shape. A theoretical method is presented to predict the non-uniform wrapping process of a metallic tape spring based on classical theories about the bending behavior of this type of tape spring. There are two possible shapes for a tape spring after the non-uniform wrapping process, namely a polygon or a continuous curve. The boundary lines of the two possible shapes are studied, and it is shown that the shape depends on the radius of the central cylindrical hub. A finite element model is built using the commercial software ABAQUS to verify the reliability of the theoretical model. Experimental measurement is also conducted to record the shape change process of a tape spring. The comparisons of the results of the three different methods show that they are in good agreement with each other, which means that the theoretical model can be used to predict the non-uniform wrapping behavior of the tape spring. Additionally, the behavior of four tape springs during the non-uniform wrapping process is studied, and the results show that the shapes of multiple tape springs in a coiled state correspond to that of a single tape spring. [ABSTRACT FROM AUTHOR]

• Snap-folding mechanics of differently shaped ring structures (circular, elliptical, rounded rectangular, and rounded triangular rings) under twisting loads is studied. • Various folding modes in terms of foldability, stability and snapping type are identified. • Phase diagrams of the folding modes with respect to geometric parameters are constructed. • Diagrams of the areal packing ratios are constructed using the reduced planar rod model. • The results provide mechanics insights into the ring snap-folding and can guide the design of ring-origami assembly. Ring origami is a new strategy to design bistable foldable/deployable structures by assembling multiple rings with the same geometry. The successful folding of ring origami assembly leverages the snap-folding capability of single rings. It is thus important to model the snap-folding of ring-shaped structures for the rational design of ring origami with good foldability, stability and high areal packing ratio. This paper studies the folding mechanics of differently shaped rings (circular, elliptical, rounded rectangular and rounded triangular rings) under twisting loads by developing theoretical and three-dimensional finite element analysis (FEA) models. The rod model is re-formulated for different ring geometries as two-point boundary value problem systems, which are then solved through numerical continuation, allowing one to capture complex equilibrium paths with multiple fold points. The rod model, verified by FEA simulations and experiments, can accurately, quantitatively capture the snap-folding behaviors for rings of different geometries. Using the rod model, we analyze the folding modes in terms of foldability, stability and snapping type. Phase diagrams of folding modes are then constructed with respect to geometric parameters for the ring profile and cross-section for differently shaped rings. Diagrams of areal packing ratios are obtained using the reduced planar rod model. This work provides comprehensive mechanics insights into the ring folding through twisting and can guide future ring origami design. [ABSTRACT FROM AUTHOR]

In this paper, a novel nonlinear viscoelastic constitutive model is proposed to describe the mechanical behavior of a polymer matrix composite (HTPB propellant). The model is built upon two stress-dependent nonlinear functions within the hereditary integral formulation of viscoelasticity. After implementation into a finite element code, the proposed model is utilized to simulate the stress-strain responses of cyclically loaded HTPB propellant. The results show that the model is capable of capturing the main characteristics of the hysteresis loops during fatigue process and good quantitative agreement is found under circumstances that self-heating effect is not evident. This paper deepens the understanding of the nonlinear behaviors of composite propellant under cyclic loading. [ABSTRACT FROM AUTHOR]

• MSG is applied for the first time to the homogenization of masonry. • The results agree with numerical or theoretical methods, including a 3D FEA. • MSG considerably reduces the computational cost. • 3D properties are obtained from the solution of 2D problems. • Absence of necessity of applying boundary conditions. Masonry is a composite material formed by units and joints, highly anisotropic and difficult to characterize. This paper presents the application of Mechanics of Structure Gene (MSG) to the homogenization of masonry. Since it is a semi-analytical technique, MSG considerably reduces the computational cost and maintains the same precision of three-dimensional (3D) analyses, for example, by the Finite Element Method. Other interesting features are the possibility of obtaining 3D properties from the solution of 1D or 2D problems and the absence of necessity of applying boundary conditions. In the analyzed examples, the 3D elastic constants of the masonry, considered as an anisotropic material, are calculated from Young's modulus and Poisson's ratio of the blocks (or units) and the mortar joints, considered as isotropic. The results obtained are compared with numerical or theoretical methods by different authors, including a 3D finite element analysis, and present agreement, even for large ratios between Young's moduli of blocks and mortar. Thus, the results presented in the paper show that the MSG method can be successfully applied in the homogenization of masonry and presents advantages over other methods for the same purpose. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamic modeling and analysis of rotating pretwisted structures with varying speed, considering complex geometries and setting angles. For thin structures with large curvature and pretwist, a modeling approach with high accuracy and efficiency is needed to capture their highly coupled vibratory behaviors. Therefore, there exists a clear demand for refining beam models with only few additional parameters to describe the shell-like performance. In this paper, we propose a novel three dimensional (3D) pretwisted beam element formulation based on the Carrera unified formulation (CUF) theory. The formulation is implemented to the coupled vibration studies of varying speed rotating pretwisted structures by describing the displacement field in rotating coordinate systems. Using nonlinear strain-displacement relations and Hamilton's principle, a 3D pretwisted beam model is derived on the basis of refined beam theories. Also the inertial, centrifugal and Coriolis effects are taken into account, so that the established model is able to reveal coupled dynamic responses, including in-plane, out-ofplane and torsional deformations. Numerical simulation is performed to study the dynamic characteristics and time responses of a fan blade and a space boom. Results show that this method accurately captures the periodic motions and unstable motions of rotating structures. Compared with traditional theories and finite element analysis (FEA) software, the proposed method significantly reduces the computational cost by using self-adaptive model order and element number. In summary, the proposed method can be used to study dynamics of varying speed rotating pretwisted structures in a precise, flexible and numerically economical fashion. [ABSTRACT FROM AUTHOR]

• Four structural types of GFRP-aluminum alloy adhesive joints were designed. • The load-bearing capacity of the designed adhesive joints was greatly improved. • Mechanical interlocking designs can delay adhesive layer failure. Enhancing the bonding strength between composites and metals is one of the urgent challenges that needs to be addressed. One of the methods to improve the strength of adhesive joints is to change the geometry of the joints. In this paper, four different types of aluminum alloy sleeves were developed by designing grooves with varying angles and shapes. Glass fiber reinforced polymer rods were adhesively bonded to these sleeves, resulting in the preparation of five different types of adhesive joints, including a conventional structure. The mechanical performance and failure mechanisms of these joints were analyzed experimentally and numerically. The results indicate that, compared to conventional adhesive joints, the load-bearing capacity of the four designed adhesive joints has been significantly improved, with a maximum increase of 49.6% and a minimum increase of 35.6%. The axial angle of the groove structures designed within the joint is a factor that influences the ultimate load capacity of the joint. Furthermore, the shear stress in the adhesive layer is identified as the primary cause of adhesive layer failure. The designed mechanical interlocking structures can not only increase the interfacial bonding force between the adhesive layer and the substrate but also delay the complete failure of the adhesive layer, thereby improving the load-bearing strength of the joint. This work is expected to provide new insights for the design of composite and metal joints. [ABSTRACT FROM AUTHOR]

[Display omitted] • A concurrently coupled model which combines dislocation dynamics and finite element method is developed. • Our model is validated with multiple test cases, showing the fidelity by computing long- and short-range stress field. • Our model could carefully consider the rotation of crystal/material coordinate systems. • Our model could capture dynamic evolution of of not only dislocations, but also interactions with other defects. • The proposed model could consider complex geometry and loading conditions, together with potential applications to multiphysics problems. The collective motion of defects and their interaction are the basic building blocks for plastic deformation and corresponding mechanical behaviors of crystalline metals. Especially, dislocations among various defects are the "carrier" of plastic deformation in many crystalline materials, particularly ductile materials. To get a fundamental understanding of plastic deformation mechanisms, it calls for an integrated computational platform to simultaneously capture detailed defects characteristics across several length scales together with corresponding macroscopic mechanical response. In this paper, we present a three-dimensional mesoscale defect dynamics model to directly couple the three dimensional discrete dislocation dynamics model with continuum finite element method, aiming at capturing both size dependent plasticity at micron-, and submicron scale and constitutive behaviors at larger scales where such size-dependence disappear. Using non-singular dislocation theories, our model could accurately consider both short- and long-range elastic interactions between multiple dislocation segments with even higher computational efficiency than traditional dislocation dynamics simulations, together with the careful consideration of crystal/material rotation in the coupled framework. In addition, our model could directly model dislocation nucleation from stress concentrators such as a void, crack and indentor tip, which could allow us to investigate various defects' motion and their mutual interactions, predicting macroscopic mechanical response of complex structures. The developed concurrently coupled model could also consider multiphysical phenomena by solving coupled governing equations in finite element framework, which could shed light on complex defect behaviors under various physical environments. [ABSTRACT FROM AUTHOR]

The crystal plasticity-based finite element method is widely used, as it allows complex microstructures to be simulated and allows direct comparison with experiments. This paper presents the OXFORD-UMAT for Abaqus®, a novel crystal plasticity code that is publicly available online for researchers interested in using crystal plasticity. The model is able to simulate a wide range of materials and incorporates two different solvers based on the solution of slip increments and Cauchy stress, with variants of state update procedures including explicit, semi-implicit, and fully-implicit for computational efficiency that can be set by the user. Constitutive laws are available for a range of materials with single or multiple phases for slip, creep, strain hardening, and back stress. The model includes geometrically necessary dislocations that can be computed using finite element interpolation functions by four alternative methods, including the total form with and without a correction for the dislocation flux, a widely used rate form, and a slip-gradient formulation. In addition, the initial strengthening and subsequent softening seen in irradiated materials can also be simulated with the model. The analysis is available in 2D (plane stress and plane strain) and 3D, including linear and quadratic elements. Here we include full derivations of the key equations used in the code and then demonstrate the capability of the code by modeling single-crystal and large-scale polycrystal cases. Comparison of OXFORD-UMAT with other available crystal plasticity codes for Abaqus® reveals the efficiency of the proposed approach, with the backup solver offering greater versatility for handling convergence issues commonly found in practical applications. • A computationally efficient and modular crystal plasticity solver scheme relying on two different solvers. • Single crystal models for slip, creep, strain hardening, length scale dependence, back stress and irradiation resistance. • Overview of crystal plasticity equations with derivations. [ABSTRACT FROM AUTHOR]

Topological interlocking assemblies (TIA) are arrangements of blocks kinematically constrained by a fixed frame, such that all rigid body motions of each block are prevented by the neighbouring blocks and the frame. In the literature, several blocks are introduced that can be arranged into interlocking assemblies, however only few of them can be arranged in non-unique ways. This study investigates a particularly versatile interlocking block called the Versatile Block: this block can be arranged in three different doubly periodic ways given by wallpaper symmetries. We investigate the hypothesis that the arrangement of copies of the same block influences the mechanical response of a TIA. We examine the interlocking mechanism and the correlation between arrangement and overall structural performance in planar TIA consisting of the Versatile Block. Furthermore, we analyse load transfer mechanisms within the assemblies and from the assemblies onto the frame. For fast apriori evaluation of the load transfer onto the frame we introduce a combinatorial model called Interlocking Flows. To investigate our assemblies from a mechanical point of view we conduct several finite element studies. These reveal a strong influence of arrangement on the structural behaviour, for instance, an impact on both the point and amount of maximum deflection under a given load, thereby confirming our hypothesis. We also evaluate the accuracy of the proposed Interlocking Flow model by a comparison with the finite element simulations. • Three different symmetric arrangements of Versatile Block studied. • Introduced novel combinatorial tool 'Interlocking Flows' for fast evaluation of assemblies. • FEM investigations: arrangement significantly impacts structural behaviour of assemblies. • 'Interlocking Flows' predict load transfer patterns accurately. • Interlocking mechanism of the Versatile Block investigated. [ABSTRACT FROM AUTHOR]

• Planar curved beam and serpentine structure may deform significantly before buckling. • A buckling theory considering finite prebuckling deformation is established. • A geometrically-nonlinear-analysis-based simulation is used to verify the theory. • Example study shows that prebuckling deformation can enhance buckling resistance. • Cross-section aspect ratio governs the effect of prebuckling deformation. The serpentine structure with a sufficiently thick cross section has recently been proposed as an important design concept in stretchable electronics, which features mechanically stable in-plane deformation mechanism and very low electrical resistance, bringing unique advantages for devices compared with the traditional thin ribbon layout. However, unduly increasing the thickness is well known to sacrifice the overall flexibility and functionality of devices. Such a contradiction leads to challenges in structural stability, as a relatively thick but insufficient serpentine structure may eventually undergo the out-of-plane buckling after significant in-plane prebuckling deformation and appreciable alterations in initial configuration, which is ignored by most conventional buckling theories (CBTs) and linear buckling analysis in commercial finite element analysis software, producing intolerable errors when predicting the critical loads. In this paper, a systematic and straightforward theory considering the finite prebuckling deformation (FPD buckling theory) is established to investigate the underlying mechanism. Two sets of governing equations related to the prebuckling and FPD buckling behavior are obtained. Four representative examples, including two classical problems of planar curved beams and two typical loading conditions of serpentine structures, have been carefully studied. Comparisons with the accurate geometrically-nonlinear-analysis-based (GNAB) buckling analysis have amply demonstrated the validity of our theory in predicting the reinforcement effect of prebuckling deformation on the buckling resistance of structures. Key dimensionless geometric parameters that govern this effect have also been identified, providing direct and effective guidance for the design and optimization of stretchable electronic devices. [ABSTRACT FROM AUTHOR]

• A prediction model of grain strain variations due to a specific neighborhood is proposed based on FE simulation observations. • A Cellular Automaton (CA) model is developed using this model and the approximations proposed in Part 1. The methodology to identify the model parameters and the model algorithm are fully described. • Studied polycrystals are represented by a regular structure (Kelvin structure) where all grains are of identical shape and size. • Both CA and FE polycrystalline aggregate stress fields predictions show very close results, but with a really shorter amount of CPU time for the CA model. • Using the quickness of the CA model, orientations causing stress concentrations were easily identified and have shown in the worst scenario to generate in a grain a resolved shear stress concentration twice more significant than for any other grains of the aggregate, without showing any different macroscopic behavior nor crystallographic texture. This paper presents the development of a Cellular Automaton (CA) capable of describing polycrystalline structures heterogeneous behavior in the elastic domain. Based on Eshelby's inclusion problem, this model is the first step to a better consideration of heterogeneities in polycrystals by including the neighborhood effect in grain's behavior. Neighborhood effects have been defined, quantified, and approximated from observations made in the first of this two-part paper, using finite element method (FEM). Considering these approximations, and based on FEM simulations results, an analytical model of the neighborhood effect was proposed in the present paper on which the CA model was built. As a first step in the model development, a regular aggregate structure (Kelvin structure) is used where grains are considered spherical and having identical size. The stress field predictions obtained with the FEM for a polycrystalline aggregate submitted to an elastic loading were compared with the CA predictions, grain by grain, for two different crystal structures (Fe and Ti). Considering the FEM as a reference tool, CA model predictions show an excellent propensity at predicting the local stress fields in polycrystals by capturing the neighborhood effect induced by grain orientations for a low computation time cost. The CA model has also shown its facility to evaluate quickly a grain influence on another grain stress level, and therefore, the orientations generating high stress concentrations in a grain can be easily identified. Using this capacity, the neighborhood effect has been shown to be able to at least double a grain stress level without the material showing any particular texture. [ABSTRACT FROM AUTHOR]

Abstract Joining by plastic deformation is recognized as a promising technique to produce laminate metal composites. In this technique, metallic layers are joined together through a metallurgical bond created by severe plastic deformation. Obviously, the accurate design of these processes requires adequate numerical tools which take into account the most important factors affecting the bond formation. In this paper, first, the mechanism of joining by plastic deformation is outlined. Then, based on the microscopic description of solid-state welding, an extended version of a cohesive zone element is introduced to describe both bonding and debonding processes in finite element modeling. In this element, the bond strength between metallic layers is calculated based on the governing parameters of the bonding process such as pressure, plastic deformation and surface cleanness. Subsequently, the mathematical formulation of the introduced element and its finite element implementation are presented. Finally, a numerical example is given to demonstrate the applicability of the proposed method in cold roll bonding processes. The element formulation introduced in this paper can be adopted by other finite element subroutines to simulate the process of bonding and debonding in engineering applications. [ABSTRACT FROM AUTHOR]

• A finite element model to simulate the lined pipe wrinkles is developed. • The manufacturing process of the lined pipe is considered in the paper. • The different effects of friction on two types of wrinkles are investigated. • The effect of friction on maximum amplitude of wrinkles is investigated. Transporting corrosive hydrocarbons using lined pipe is an economical method and has been widely applied in inshore and offshore pipelines. However, when the lined pipe is subjected to bending, wrinkling behavior will occur. Wrinkle can pose a serious threat to the service life and structural integrity of the lined pipe. In this paper, the effect of the friction coefficient between the liner and carrier on the wrinkling behavior of liner under bending is studied. First, a finite element model of lined pipe is established. Second, the influence of friction coefficient on the starting time and amplitude of first type of wrinkles is studied. In the end, the influence of friction coefficient on the amplitude and shape of the second type of wrinkles is examined. The results show that the friction coefficient can affect both the first and the second type of wrinkles, but their effects are different. The friction coefficient can contribute to the first type of wrinkles. Friction coefficient will facilitate the appearance of the first type of wrinkles. While, the friction coefficient showed a strong inhibitory effect on the second type of wrinkles, which inhibited the maximum amplitude and shape of the wrinkles. [ABSTRACT FROM AUTHOR]

This paper addresses the effect of wire slipping on the mechanical properties of structural cables. Based on parameter calibration with experimental data, the paper proposes a Finite Element modelling framework aimed at enhancing the prediction accuracy of the stick/slip behaviour of semi-parallel wire (SPW) cables. The model considers the specific arrangement of the SPW cable composition, interwire friction, and residual interlock between wires. Gaussian Process regression is employed as a surrogate model to reduce the model's computational cost, optimise parameters and quantify uncertainty. The results show high prediction accuracy when compared with experimental data for different pretension forces. The study finds that wire slip varies considerably between wire layers and is significantly influenced by residual interlock between wires. Additionally, cyclic loading under high bending curvatures reveals that the hysteresis behaviour is dependent on wire slip and loading history. The proposed model accurately predicts the stick/slip behaviour of SPW cables, emphasising the importance of accounting for wire slipping in cable analysis models for various applications. • A proposed FEM framework for accurate prediction of stick/slip behaviour of large diameter semi-parallel wire cables. • Gaussian Processes used to reduce computational cost and quantify uncertainty. • Significant influence of residual interlock between wires on stick/slip and hysteresis. • Residual cohesion interlock is significantly higher in the inner wire layers. • Wire slip is dependent on bending curvature and loading history. [ABSTRACT FROM AUTHOR]

In neural network-based methods for elasticity mechanics such as Physics-Informed Neural Networks (PINNs), the training process is typically time-consuming due to multiple optimization iterations and reliance on automatic differentiation for gradient computation. This paper proposes a novel framework that combines Physics-Informed Extreme Learning Machines (PIELM) with linear elastic mechanics, focusing on the integration of discretization operators with the principles of linear elasticity mechanics. These discretization operators are constructed based on the form of higher-order derivatives in PIELM, along with governing equations and boundary conditions. Physical information is incorporated into the loss function through discretization operators applied at collocation points. The solution of the proposed method is calculated through the least squares method , which determines the output weights. The comparison with PINN under nonlinear loads and geometric defects demonstrates that PIELM achieves superior error control and prediction accuracy. Furthermore, PIELM achieves more precise in evaluated error norms compared to Finite Element Method (FEM) in a three-dimensional problem with an analytical solution. In conclusion, the proposed method offers an robust and efficient alternative method for linear elasticity. [Display omitted] • Developing a PIELM framework for solving linear elasticity mechanics problems. • Using discretization operators to integrate physical information into the framework. • The framework reduces hyperparameters and simplifies process compared to PINN. • The framework demonstrates advantages in terms of global error control capabilities. [ABSTRACT FROM AUTHOR]

Well-behaved nonlinear structures, which exploit elastic instabilities for functionality, have garnered increasing interest for rapid shape shifting and energy dissipation applications. One of the current bottlenecks during design is the large computational cost associated with nonlinear solvers when targeting a specific function through inverse design. Advances in machine learning (ML) tools have enabled a more efficient inverse design process. However, generating sufficient data efficiently to train the ML models still remains a challenge. This paper presents a novel computational toolbox that automates the generation of nonlinear finite element models, submission of analyses, monitoring of ongoing analyses, termination of analyses upon meeting specified criteria, and post-processing of results. With this computational toolbox, we develop three types of ML models: two forward models that classify and characterise nonlinear equilibrium paths based on the structure's properties (material and geometry), and one backward model for predicting the structure's properties from key features of the nonlinear equilibrium path. We evaluate various ML algorithms for each model type, provide recommendations, and explore algorithmic modifications to enhance prediction accuracy To illustrate the effectiveness of the proposed tools, we present two case studies where the von Mises truss plays a key role: (a) a recoverable energy dissipating mechanical metamaterial and (b) a vibro-impact capsule robot. Our findings highlight the potential of data-driven approaches to efficiently enable the design of high-performance nonlinear structures that harness instabilities for targeted functionalities. • Developed classification surrogate models to distinguish different nonlinear behaviours. • Created forward and inverse surrogate models for efficient design/analysis. • Integrated optimisation and machine learning for performance-based design. • Demonstrated applications in energy dissipation metamaterials and capsule robots. [Display omitted] [ABSTRACT FROM AUTHOR]

Highlights • A general parameterization and a new analytic model of a honeycomb are proposed. • The radius of the inclined walls and the adhesive layer influence are considered. • Besides flexure, stretching, and shearing the mechanism of hinging is included. • In plane elastic constants are compared to those from a FEA reference solution. • The advantages and limitations of the model are presented in a case study. Abstract In the present paper a general parameterization of a periodic hexagonal honeycomb with double vertical walls (commercial honeycomb) is proposed and a new analytic model is established. More attention is paid to account for the radius of curvature of the inclined walls, the adhesive layer thickness, and adhesive fillet at nodes. Then, neglecting the skin effect, in plane elastic constants is obtained analytically using the beam theory. The deformation mechanisms of the honeycomb cells include flexure, stretching, shearing and hinging. The mechanism of hinging is included through small fictitious beams in order to balance the local effects which cannot be captured using the beam theory. Hinging can be neglected when the thickness of these beams becomes infinite or optimally chosen by a proper thickness as to minimize the cumulative errors of the analytical assumptions. The new analytic model presented in this paper can be particularized to the extended Balawi and Abot model if some parameters are adequately modified. The finite element modeling of a representative volume element is used for model calibration and validation considering different relative densities of real honeycombs. The numerical results obtained as a reference for the effective elastic constants are discussed by comparing them to the ones given by the analytic model; its advantages and pitfalls are discussed and explained through a case study and some sensitivity analyses. Numerical simulations are also done in order to establish the distribution of the stresses in cell walls and nodes to confirm the hypotheses used for determining the analytical relations and to explain some limits of the analytic model. The results provide new insights into understanding the mechanics of honeycombs and facilitate the design of new types of cellular materials, including composite hexagonal cell cores. Graphical abstract Image, graphical abstract [ABSTRACT FROM AUTHOR]

This paper addresses the buckling behaviour of a long thin orthotropic plate on a tensionless rigid foundation under combined in-plane shear and bending, where the sheet can only buckle away from the foundation due to the tensionless foundation support. Two boundary conditions at the longitudinal edges ( y  = 0 and b ) are investigated, i.e. clamped and simply supported. The energy method is used to derive the explicit expression for the lateral buckling mode function. The buckling response is then obtained by solving the governing differential equation after substituting the lateral buckling mode function. Based on the analytical solutions developed in the paper, fitted formulae are given for buckling coefficients and the interaction curve. Finally, a numerical example of a corrugated sheet is given to verify the presented model through comparing the results with finite element (FE) analysis. [ABSTRACT FROM AUTHOR]

This paper proposes a simple, yet effective, modified crystal plasticity framework which is capable of modelling plasticity and creep deformation. In particular, the proposed model is sufficiently versatile to capture the effects of complex load histories on polycrystals, representative of those experienced by real materials in industrial plant. Specifically, the methodology was motivated by the need in the power generation industry to determine whether cyclic pre-straining influences the subsequent creep behaviour of type 316H austenitic stainless steel as compared to non-cyclically pre-strained material. Cyclic pre-straining occurs widely in plant and it is of paramount importance to accurately account for its impact on the subsequent deformation and integrity of relevant components. The framework proposed in this paper considers the effects of dislocation glide and climb in a relatively simple manner. It is calibrated using experimental tests on 316H stainless steel subjected solely to monotonic plasticity and forward creep. Predictions are then obtained for the creep response of the same material after it had been subjected to cycles of pre-strain. The predictions are compared to experimental results and good agreement was observed. The results show slower creep strain accumulation following prior cyclic loading attributed to hardening structures developed in the material during the cyclic pre-strain. The model also highlights the importance of accounting for directionality of hardening under reverse loading. This is hypothesized to affect the development of an internal stress state at an intragranular level which is likely to affect subsequent creep accumulation. [ABSTRACT FROM AUTHOR]

• Nematic-genesis polydomain nematic elastomers (N-PNEs) can be energy absorber. • Voronoi diagram-based finite element model is established for N-PNEs. • Cyclic tensile and compressive behaviors of N-PNEs is investigated numerically. • Smooth polydomain-monodomain transitions and memory effect are captured. • N-PNEs show superior energy absorption and dissipation than monodomain ones. Nematic elastomers (NEs) are lightly cross-linked elastomers with nematic mesogens integrated in their polymer networks. Combination of large deformation capability with nematic-isotropic phase transition enables NEs to be the most promising soft materials for impact attenuation, actuation and soft robotics. In this paper, we focus on nematic-genesis polydomain NEs (N-PNEs) where mesogens are cross-linked at nematic states. N-PNEs are capable of absorbing and dissipating energy and easy to synthesize. We present a Voronoi diagram-based finite element model for specimen-scale N-PNEs, and investigate the cyclic tensile and compressive behaviors of N-PNEs at different strain rates. Our simulations reveal a smooth polydomain-monodomain transition during loading, accompanied by a full recovery of polydomain texture after the load is removed, indicating a memory effect of initial disordered mesogen alignment. The predicted behaviors align well with experimental observations, which validates our model. Furthermore, we assess the energy absorption and dissipation capabilities of N-PNEs compared to monodomain NEs, identifying conditions where N-PNEs exhibit superior performance. This study not only enhances our understanding of polydomain-monodomain transitions in N-PNEs, but also lays the groundwork for the development of N-PNE-based energy absorbers. [ABSTRACT FROM AUTHOR]

In this paper, a new algorithm to solve the elastic quarter-space, the eighth-space and the finite-length-space contact problems is proposed. This corresponds to an extension of the Hertz theory. The theoretical foundations of such a problem are limited, due to the presence of displacements at the free edges- or stresses at the virtual edges — resulting to complex boundary conditions. The new approach presented here is 3D and based on Guilbault's ingenious fast correction method. In this approach, the edge effects are taken into account by introducing two corrective factors ψ 1 , ψ 2 respectively on the (O x) and (O z) axes to replace the mirror pressure iterative process of Hetenyi. The exact numerical values of these two correction factors are derived analytically. The results show that the free edge can substantially increase locally the contact pressure and therefore the stresses and displacement fields if close to the contact area. So the pressure field and the contact zone present an asymmetry which is more pronounced as the free edge is getting closer. This study is carried out on spaces with one, two and four free edges which will be respectively called: quarter-space, eighth-space and finite-length-space. A validation is performed using a Finite Element Method (FEM) analysis. A parametric study is also performed to exhibit the differences with the Hertz solution, including in the situation where one expects the truncation of the contact area when the free edge is virtually located within the Hertz contact area. • A new algorithm to solve the elastic finite space contact problem is proposed. • Two corrective factors called ψ 1 and ψ 2 are derived from hyper-geometric series. • Surprisingly the contact print moves away from the free edge when it comes closer. • The maximum contact pressure increases when the free edge comes closer. • The model has been validated with the Finite Element Method. [ABSTRACT FROM AUTHOR]

The quantification of uncertainties in the mechanical response of composite structures can be a computationally demanding task. This is due both to the number of uncertain parameters in a real study case and the complexity of the model to be analysed. In this paper, an efficient global/local approach to estimate the uncertainties of the quantities of interest in specific regions of interest with limited computational effort is proposed. This is achieved by refining only locally the model taking advantage of Refined Structural Theories. At the same time, since the variance of the uncertain parameters is usually relatively small, the stochastic analysis is dealt with a sensitivity study carried out both in the global and in the local model. In this way, it is possible to assess the influence of global and local uncertain parameters in the same submodeling analysis. The methodology presented is applied to several study cases of interest. The results focus on obtaining probabilistic distributions of the stress field that can be later used in failure criteria to evaluate the subsequent distribution of the failure index. Furthermore, a damage tolerance study case is investigated, showing good correlation with the reference Monte Carlo simulations. • Uncertainty Quantification via a stochastic perturbation method. • Computationally efficient methodology to assess damage initiation. • Good correlations with reference Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

Dielectric elastomer minimum energy structures (DEMES) have attracted significant attention in the recent past because of their ability to switch between multiple equilibrium states. The DEMES is formed when a pre-stretched elastomer film adheres to an inextensible frame and is further allowed to attain an equilibrium configuration as a result of energy minimization. While several researchers have investigated; both theoretically and experimentally, the underlying mechanics of DEMES, a majority of them deploy simplistic boundary frames (square/rectangular/circular) to obtain the requisite minimum energy configuration. In this paper, we demonstrate that this seemingly restrictive choice of using simplistic frame geometries can be given away by designing more complex-shaped compliant frames capable of producing useful modes of deformation. To demonstrate this idea, two prototypes; namely, the four-arm gripper actuator and the flapping-wing actuator, are studied numerically and experimentally. In both cases, a single compliant frame is used to realize the respective configuration, thus circumventing the need to assemble multiple MES on a common platform. In tandem, we investigate the role of reinforcements in (a) controlling the warping in MES and (b) maximizing actuation in the desired mode of deformation. Finite element analysis are carried out using the ABAQUS to determine the equilibrium configuration of the actuators, and subsequently their electromechanical behavior. Experimental investigations involve the utilization of the commercially available VHB 4910 acrylic tape in conjunction with PET frames and 3D-printed reinforcements. Excellent qualitative agreement is achieved between the numerical predictions and the experimental observations. Finally, we allude to a few innovative frame architectures leading the MES of engineering interest. • Design of dielectric elastomer minimum energy structures (DEMES) by using a single complex-shaped compliant frame. • DEMES-based four-arm gripper and flapping-wing actuators are studied numerically and experimentally. • To induce anisotropic properties in the specimen, 3D-printed reinforcements are strategically employed. • Investigate the role of reinforcements in controlling the warping in MES and maximizing actuation in the desired mode of deformation. [ABSTRACT FROM AUTHOR]

• A co-rotational framework is proposed for the analysis of tensegrity-membrane structures. • Wrinkling of membrane is modeled based on the Tension Field Theory. • Cluster actuation is introduced for attitude control. • Numerical examples and experiments were utilized to validate the accuracy and reliability. • Surrogate model-based optimization is achieved for the modulation of wrinkling. Tensegrity-membrane structures are potential to be lightweight gossamer spacecraft (e.g., solar sails, radar antennae, solar module), and the dynamics of deployment has been studied in the past studies where the membranes were usually modeled as a flat panel without wrinkles. However, the attitude control of membrane as well as the flatness are critical to the functionality of gossamer spacecraft. The paper proposes a numerical investigation on the modulation of wrinkling in tensegrity-membrane structures. The kinematic and deformation description is based on the co-rotational finite element method (FEM), while the wrinkling of membrane is modeled by Tension Field Theory (TFT). The numerical method is validated by an illustrative experiment, and then used for a surrogate model-based optimization design, in which clustered actuation is responsible for the attitude control of membrane, while classical actuation accounts for the suppression of wrinkles. An interesting tensegrity-membrane "Sunflower" is presented to show the result of optimization, where "Sunflower" can follow the sunlight angle accurately and freely control the orientation of "corolla" while maintaining its daylighting surface quality. This study provides an effective means for the numerical simulation and optimization design of tensegrity-membrane structures, especially when the attitude and wrinkling of membranes must be considered. [ABSTRACT FROM AUTHOR]

• Novel zero-macrospin co-rotational approach for 3D continuum finite elements. • Formulation simplicity via deformation gradient defined at macro element level. • Full derivation with symmetric geometric stiffness matrix arising naturally. • Exposition of misconceptions and errors in Crisfield's seminal asymmetric formulation. • Demonstration of computational superiority of proposed symmetric formulation. The seminal work of Crisfield on co-rotational finite elements came to a profound conclusion that the geometric stiffness matrix of 3D continuum finite elements is inherently asymmetric, though it becomes symmetric under equilibrium conditions. Contending that these outcomes are misconceptions, this paper presents a novel zero-macrospin co-rotational approach for 3D continuum elements in which the geometric stiffness matrix is always symmetric for work-conjugate conservative loads, suggesting that Crisfield's geometric stiffness is erroneously asymmetric and inconsistent. This contention is subsequently upheld by identifying crucial terms omitted in Crisfield's formulation which are responsible for the erroneous asymmetry, and the notion that symmetry is eventually recovered at equilibrium is shown to be a further misconception. Importantly, this critical appraisal of Crisfield's formulation, which has been adopted by numerous researchers, and the delineation of its underlying misconceptions exceed academic interest to real practical relevance. Several numerical examples are presented in the paper which highlight the superiority of the proposed approach, lending incontrovertible practical evidence that the consistent geometric stiffness matrix for co-rotational 3D continuum elements is always symmetric for work-conjugate conservative loads. [ABSTRACT FROM AUTHOR]

Abstract: The mechanical behavior of fibrous networks is governed by complex multiple mechanisms. This study examines the effect of microstructure on the macroscopic deformation and fracture of two-dimensional random fiber networks and its practical implications for understanding the material failure in paper materials by using finite element models. Remote load is a pure mode I opening field, applied via a boundary layer. Characteristic networks, consisting of the union of solutions of several unique networks, are interpolated on a rectangular grid covering the whole problem domain. The interpolated solutions are interpreted as network-equivalent continuums representing the mechanical behavior, on average, for a specific set of structural properties. A regularization routine is included in a variational procedure in order to minimize potential energy in the body and produce continuous strains at cell borders in the grid. It is shown that using a classical continuum linear elastic fracture mechanics (LEFM) approach to describe macroscopic singular-dominated fields in fiber networks, can lead to erroneous results especially in networks having a low degree of bonds per fiber. The classical continuum description is too simple to capture the essential mechanical behavior for this class of material since a structural effect, that alters the displacement field, becomes pronounced. It is necessary to include a nonlocal theory to describe the mechanical behavior at a continuum level. By using an appropriate characteristic length in a nonlocal continuum formulation, strain energies, in the neighborhood of a dominant macroscopic singularity, are calculated that agree well with characteristic network models and hence produce fairly good agreements between the networks and the nonlocal continuum models. A key conclusion found is that, only for networks with a high degree of bonding, can the mechanical behavior around a macroscopic singularity be captured by the classical local continuum theory. In networks with a low degree of bonds per fiber, there are regions far away from the macroscopic singularity that have relatively higher magnitudes of strain energy than predicted by the classical theory. A relation between an internal length scale parameter, used in the nonlocal continuum model, and the structural properties of the network is approximated by a simple function. [Copyright &y& Elsevier]

Abstract: Finite element analysis of ink-tack delamination of paperboard were presented. The paperboard was modeled as a multilayered structure with a softening interface model connecting the paperboard plies. The paperboard plies were modeled as orthotropic linear elastic. The ink-tack loading was applied to the board in the form of a moving displacement boundary condition. The purpose of the analysis was to assess the influence from the elastic moduli of the individual layers on the ink-tack delamination event. The results indicated that in most cases of practical interest the board delaminated between the outer plies of the board, although the interface strength was lower in the middle of the board. This observation helped to explain why traditional tests for out-of-plane testing of paper by standardized methods could not uniquely predict the propensity for ink-tack delamination. [Copyright &y& Elsevier]

This paper is dedicated to creep buckling predictions. Thin walled cylinders having an aspect ratio of one are subjected to an uniform external pressure. The material is a special type of nickel which “creeps” at ambient temperature. The material parameters for the creep law are identified from experimental results. The creep failure experiments are described and corresponding failure times are given. The paper then compares three alternatives of finite element modeling of the experiments (3D Shell with integration through the thickness with a periodic or non periodic initial imperfection are compared with COMU quasi axi-symmetric imperfect shell element). These 3 modeling show consistent predictions. The simulation time is a hundred times faster with the COMU model. It is shown that the prediction of failure time of these experiments is extremely sensitive to the initial imperfection amplitude. The effect of creep law modeling is also important. Finally a parametric analysis on different types of cylinders is given: some general trends are proposed for this type of delicate predictions. [ABSTRACT FROM AUTHOR]

This paper presents a study on the metal cutting simulation with a particular numerical technique, the Particle Finite Element Method (PFEM) with a new modified time integration algorithm and incorporating a contact algorithm capability . The goal is to reproduce the formation of continuous chip in orthogonal machining. The paper tells how metal cutting processes can be modelled with the PFEM and which new tools have been developed to provide the proper capabilities for a successful modelling. The developed method allows for the treatment of large deformations and heat conduction, workpiece-tool contact including friction effects as well as the full thermo-mechanical coupling for contact. The difficulties associated with the distortion of the mesh in areas with high deformation are solved introducing new improvements in the continuous Delaunay triangulation of the particles. The employment of adaptative insertion and removal of particles at every new updated configuration improves the mesh quality allowing for resolution of finer-scale features of the solution. The performance of the method is studied with a set of different two-dimensional tests of orthogonal machining. The examples consider, from the most simple case to the most complex case, different assumptions for the cutting conditions and different material properties. The results have been compared with experimental tests showing a good competitiveness of the PFEM in comparison with other available simulation tools. [ABSTRACT FROM AUTHOR]

The present paper addresses the challenge of conducting Finite Element (FE) micromechanical simulations based on 3D X-ray data, and quantifying errors between simulations and experiments. This is of great interest, for example, in the study of ductile fracture as local comparisons and error indicators would help understanding the limitations of current plasticity and damage models. Standard methods used in the literature to conduct FE simulations at the microscale are often based on multiscale schemes. Relevant mechanical fields computed in an FE simulation at the specimen scale are used as boundary conditions for the micromechanical simulation, where the real microstructure is meshed from 3D X-ray images. These methods hence rely on an identification of material behavior at the macroscale, say, using force measurements and 2D surface images. In an earlier work by the authors, a method for conducting micromechanical simulations using measured boundary conditions thanks to Digital Volume Correlation (DVC) was proposed. The interest of this DVC-FE approach is that it uses solely 3D X-ray images acquired in-situ during the experiments. Thus, FE simulations are directly conducted at the microscale, with no dependence on specimen scale simulations or multiscale schemes. This approach also includes a methodology to perform local error measurements with respect to experimental observations. In this paper, both multiscale schemes and this DVC-FE approach are applied to new experimental results on a nodular graphite cast iron specimen with machined holes. Ductile fracture due to the nucleation, growth and coalescence of microscopic voids between the machined holes is observed in-situ thanks to synchrotron 3D imaging. The objective of this paper is to assess the accuracy of boundary conditions for each approach and conclude on the optimal choice. Based on both average and local error measurements, it is shown that void growth is underestimated with multiscale schemes, while predictions are significantly improved with the DVC-FE approach. [ABSTRACT FROM AUTHOR]

This paper presents a novel scheme to biaxially package and deploy flat membranes, in which the thickness of the membrane is accounted for through the novel concept of slipping folds. The membrane is divided into parallel strips connected by slipping folds, and specially chosen wrapping profiles that require zero slip along the edges of the membrane are identified. This packaging scheme avoids the kinematic incompatibilities that in other schemes result in local buckles and wrinkles that increase the deployment force and permanently deform the membrane. The paper also presents a scheme to apply uniform uniaxial prestress to the deployed membrane, as well as a two-stage deployment scheme. Packaging efficiencies of up to 83% have been demonstrated for meter-scale models, although for large membranes the packaging efficiency approaches 100%. [ABSTRACT FROM AUTHOR]

• A new simulation framework based on the PINNs is presented for modelling crack problems. • An enriched PINNs is proposed to correctly capture the local crack-tip behavior. • The SIFs can be directly calculated with very high accuracy. • A deep-learning algorithm written in MATLAB is provided. In this paper, a method based on the physics-informed neural networks (PINNs) is presented to analyze 2D in-plane crack problems in the linear elastic fracture mechanics. Instead of using a discretizing mesh, the PINNs-based method is meshless and can be trained on batches of discretely sampled collocation points. In order to capture the asymptotic behavior of the near-tip displacement and stress fields, the standard PINNs formulation is enriched here by including the crack-tip asymptotic functions such that the local behavior in the crack-tip region can be modeled accurately without a nodal refinement. The trainable parameters of the enriched PINNs are learned to satisfy the governing partial differential equations of the cracked elastic solid and the corresponding boundary conditions. It is found that the incorporation of the crack-tip enrichment functions in the PINNs is substantially simpler and more feasible than in the conventional finite element method (FEM) or boundary element method (BEM). The present PINNs-based algorithm is tested and verified by several representative benchmark examples for different loading and crack-mode types. Numerical results show that the present PINNs-based method can provide highly accurate stress intensity factors (SIFs) with only few degrees of freedom. For interested readers, a self-contained MATLAB code and data-sets supplementing this paper are also provided in the Supplementary material. [ABSTRACT FROM AUTHOR]

• A crystal plasticity finite element model with a dislocation density-based hardening is adapted to simulate nanoindentation. • Simple compression and nanoindentation elastic slopes and yield stresses are measured and simulated for 15 Ta crystals. • Indentation to compression yield stress ratios vary with crystal orientation in the range from 2.6 to 3.6. • More slip systems activate under indentation than under compression because of a more complex stress/strain state. • Indentation yield stress is less anisotropic than simple compression yield stress. Experiments and corresponding crystal plasticity finite element (CPFE) simulations of spherical nanoindentation were performed to determine yield stress under indentation of fifteen Ta single crystals randomly distributed in the orientation space. Agreement between the measured and simulated indentation yield stresses and initial hardening slopes demonstrated accuracy of the model. Moreover, simple compression simulations were performed for the same crystals to study the differences in compressive versus indentation yielding. Ratios of the indentation to compressive yield stress were found to vary with crystal orientation in the range from 2.6 to 3.6. The simulations allowed us to reveal underlying deformation mechanisms accommodating the yielding in indentation and simple compression. It is found that more crystallographic glid mechanisms activate under indentation than simple compression owing to the more complex state of stress and strain in indentation than in compression. Owing to the activation of more glide systems in indentation than in simple compression, the indentation yield stress is less anisotropic than the simple compression yield stress. The modeling framework, simulation setups, results, and insights from the results are presented and discussed in this paper. [ABSTRACT FROM AUTHOR]

• Single surface fully coupled thermomechanical constitutive model for SMAs. • Transformation strain and entropy depends on temperature. • Inhomogeneous deformation modeled as softening. • Structural multiphysics simulations for set of isobaric tests. • Interaction of helical localization patterns and latent heat reproduces their rate. In an isobaric test, typically used for establishing the transformation temperatures of SMAs, a specimen is taken through a cool/heat cycle at a prescribed stress level. The companion paper, Part I, demonstrated that such tests on NiTi tubes result in rather complex interactions between the helical bands of localized deformation induced by phase transformations, the associated latent heat, and the thermal exchange with the environment. These interactions were quantified using accurately controlled testing conditions and full-field diagnostics, and provide a challenging platform for evaluating analyses. In Part II this challenge is met by first extending the thermomechanical constitutive framework developed by our group to include variations of transformation stress, strain, and latent heat with temperature. Unique features of the model include: modeling the reversible phase transformations of NiTi through a single surface in the deviatoric stress–temperature space with the transformation strain and entropy as the internal variables; and use of softening to model the inhomogeneous deformation exhibited in tension. The model is calibrated to the isothermal results of Part I. The constitutive model is then incorporated into a fully coupled static displacement-thermally transient finite element analysis that is used to simulate the isobaric experiments on NiTi tubes of Part I over a range of stresses. The clamped ends of the experiment are idealized as radial constraints. Heat exchange between the structure and the environment is strictly by convection. Isobaric testing is simulated by taking the model tube through the cool/heat cycle of the experiment at the prescribed stress level. A small thickness depression at one of the ends is used to initiate localized transformation. The temperature-strain response is reproduced with the two transformations initiating at essentially the same temperatures as in the experiments, producing the correct transformation strains for all stress levels. Transformation of M propagates via a helical band at similar speeds as in the experiments, while transformation of A is via multipronged fronts for all cases. Successful reproduction of the velocities of the banded transformations is governed by the value of the convection coefficient. Overall, the reproduction of the isobaric experiments over a range of stress levels, validates the constitutive and structural models. It also points to the limitations of modeling the heat exchange between the specimen and the environment only by convection. [ABSTRACT FROM AUTHOR]

Microscale beam-like structures are standard components of micromechanical systems in many devices. However, the small dimensionality affects their deformation characteristics and leads to misinterpretations of the results. Presenting such size dependency is possible with advanced continuum descriptions via introducing additional variables compared to the classical one. Hence, the problems where contact occurs require the readjustment of boundary conditions considering these extra parameters. That burdens the already challenging task of contact problem calculations and restricts most demonstration examples to two-dimensional problems and geometrical linearity. The resolution of the imposed restrictions within finite element modeling further emphasizes the usage of advanced media in design and facilitates its application to various problems, which is the aim of this paper. The delivery of that task is as follows. Firstly, we present the kinematics and material descriptions for the micropolar media. The authors propose to use a newly developed continuum-based micropolar beam formulation to avoid an overwhelming computational burden and, at the same time, deal with nonlinear stress–strain relations. Secondly, the work develops a contact approach within the micropolar theory from two-dimensional to three-dimensional elasticity, although the contact is considered frictionless. Finally, it compares two existing contact formulations, including the developed one, for the contact beam problems, using the examples of two collinear sliding beams' bending. • Presented two known contact formulations within the micropolar theory. • Developed one of the contact approaches to three-dimensional elasticity. • Considered a practical problem of bending two-layered cantilever beam.. [ABSTRACT FROM AUTHOR]

This paper aims to propose a novel fracture criterion to predict complex propagation behaviors of a bimaterial interface crack, either delaminating along the interface or kinking out of the interface into one of the adjoining materials. A strength-based criterion is used to predict the crack deflection, and an energy-based criterion is adopted to assess delamination along the interface. To determine the competition between these two cracking modes, a competing strategy is developed by comparing the strength-based and energy-based criteria. This coupled strength-energy fracture criterion eliminates the disadvantages arising from a criterion based solely on strength or energy, and is convenient to be calculated and embedded into numerical models. As practice, we embed the criterion into a homemade extended finite element model to simulate bimaterial interface crack propagation. Several numerical examples are performed to verify the effectiveness and accuracy of the developed model. Finally, this model is applied to simulate an interface crack propagation in a sandwich structure that has a specially designed peel-stopper. Parametric studies reveal that the material and interface toughness as well as geometrical dimensions of the structure have significant effects on the propagation mode of the interface crack. The results provide practical suggestions on the optimal design of peel-stopper in sandwich structures. • A novel strength-energy fracture criterion is proposed for crack propagation. • The developed XFEM model embedded with fracture criterion is established. • The developed model correctly captures the crack propagation behavior. [ABSTRACT FROM AUTHOR]