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The study addresses the lack of standardization for the evaluation of the shear properties of hyperelastic soft foams. The results of three different standards used for sandwich structures or rigid materials (ASTM C 273, BS 4370, ASTM D 5379) are compared using specimens with different geometries and aspect ratios. Displacements are captured using Digital Image Correlation applying texture correlation and an incremental approach on three flame-retardant foams with densities around 85, 63, and 46 kg/m³. The study examines secondary effects like bending moments and normal stresses, finding the Iosipescu method effective for hyperelastic foams, ensuring minimal material wastage and test repeatability. [ABSTRACT FROM AUTHOR]

Background: Deformable image registration is an essential technique of medical image analysis, which plays important roles in several clinical applications. Existing deep learning‐based registration methods have already achieved promising performance for the registrations with small deformations, while it is still challenging to deal with the large deformation registration due to the limits of the image intensity‐similarity‐based objective function. Purpose: To achieve the image registration with large‐scale deformations, we proposed a multilevel network architecture FCNet to gradually refine the registration results based on semantic feature consistency constraint and flow normalization (FN) strategy. Methods: At each level of FCNet, the architecture is mainly composed to a FeaExtractor, a FN module, and a spatial transformation module. FeaExtractor consists of three parallel streams which are used to extract the individual features of fixed and moving images, as well as their joint features, respectively. Using these features, the initial deformation field is estimated, which passes through a FN module to refine the deformation field based on the difference map of deformation filed between two adjacent levels. This allows the FCNet to progressively improve the registration performance. Finally, a spatial transformation module is used to get the warped image based on the deformation field. Moreover, in addition to the image intensity‐similarity‐based objective function, a semantic‐feature consistency constraint is also introduced, which can further promote the alignments by imposing the similarity between the fixed and warped image features. To validate the effectiveness of the proposed method, we compared our method with the state‐of‐the‐art methods on three different datasets. In EMPIRE10 dataset, 20, 3, and 7 fixed and moving 3D computer tomography (CT) image pairs were used for training, validation, and testing respectively; in IXI dataset, atlas to individual image registration task was performed, with 3D MR images of 408, 58, and 115 individuals were used for training, validation, and testing respectively; in the in‐house dataset, patient to atlas registration task was implemented, with the 3D MR images of 94, 3, and 15 individuals being training, validation, and testing sets, respectively. Results: The qualitative and quantitative comparison results demonstrated that the proposed method is beneficial for handling large deformation image registration problems, with the DSC and ASSD improved by at least 1.0% and 25.9% on EMPIRE10 dataset. The ablation experiments also verified the effectiveness of the proposed feature combination strategy, feature consistency constraint, and FN module. Conclusions: Our proposed FCNet enables multiscale registration from coarse to fine, surpassing existing SOTA registration methods and effectively handling long‐range spatial relationships. [ABSTRACT FROM AUTHOR]

We present a fractional order model for nonlinear visco-hyperelastic solids taking into account large deformations. A three-field form of the Hu-Washizu principle is introduced to create a stable finite element method in the context of nearly incompressible dynamics. The β-method (a generalized midpoint rule) for time discretization is implemented into a variational finite element framework for efficient computing of numerical approximations to the initial boundary-value problem for hyperbolic equation of motion. Finally, a 2-D cantilever beam problem with a step end load is considered in order to demonstrate the algorithm. [ABSTRACT FROM AUTHOR]

A second-order multiscale theory based on the concept of a Representative Volume Element (RVE) is proposed to link a classical poromechanical model at the RVE scale to a high-order poromechanical model at the macro-scale in the context of finite-strain kinematics. The proposed theory is carefully derived from the Principle of Multiscale Virtual Power, which is a generalization of the Hill-Mandel Principle of Macrohomogeneity. The coupled governing equations of the low-scale and the homogenization rules for the flux and stress-like quantities are obtained by means of standard variational arguments. The main theoretical result is that the minimally constrained space for the pore pressure field allows for non-zero net fluid flow across the RVE boundaries, unlike first-order theories. The direct consequence of this finding is that the present theory can be consistently applied in cases where the low-scale (RVE level) exhibits substantial volume changes (swelling or shrinking) as a consequence of the evolution of the macro-scale kinematics. Details of formulation development and expression for the homogenized tangent operators are presented for those interested in the computational implementation of the model. [ABSTRACT FROM AUTHOR]

A bending study was carried out on samples of rectangular cross-section made of structural steel 10Г2 (10G2) after laser hardening and laser alloying. It has been established that the presence of a laser impact zone leads to an increase in the elastic work area of the samples within 20–30 % in accordance with the implemented material processing mode and an even more significant increase in the level of perceived maximum load.

The present study aims to develop an original solid-like shell element for large deformation analysis of hyperelastic shell structures in the context of isogeometric analysis (IGA). The presented model includes a new variable to describe the thickness change of the shell and allows for the application of unmodified three-dimensional constitutive laws defined in curvilinear coordinate systems and the analysis of variable thickness shells. In this way, the thickness locking affecting standard solid-shell-like models is cured by enhancing the thickness strain by exploiting a hierarchical approach, allowing linear transversal strains. Furthermore, a patch-wise reduced integration scheme is adopted for computational efficiency reasons and to annihilate shear and membrane locking. In addition, the Mixed-Integration Point (MIP) format is extended to hyperelastic materials to improve the convergence behaviour, hence the efficiency, in Newton iterations. Using benchmark problems, it is shown that the proposed model is reliable and resolves locking issues that were present in the previously published isogeometric solid-shell formulations. [ABSTRACT FROM AUTHOR]

The topological derivatives for shell structures in dynamic loadcases, which are often used in lightweight designs, are developed. These sensitivities consider the highly nonlinear material behavior and large deformations of the structure. The aim of the investigation is the support of an efficient topology optimization for crashloaded structures. The considered functionals can in general be described by displacements, velocities and accelerations. In particular, the semi-analytical sensitivity calculations for the internal deformation energy and for single point displacements in arbitrary directions in the shell structure are presented. These functionals cover the most important functions for the development of crash structures. Using the material derivative in combination with the adjoint method, a terminal value problem has to be solved. Depending on whether first differentiation and then discretization in the time domain is performed or first discretization and then differentiation, a separate solution scheme for the adjoint is derived. Both schemes are presented in a comparable description. For the numerical evaluation of the topological derivatives, the basic equations for large deformed shell elements are included as well as a phenomenological material interpolation, which represents the tangential material behavior resulting from plastic strain and isotropic hardening. All assumptions made for the derivation are described in detail and their influences are discussed. The elaborated equations and the procedure for the calculation of the topological derivatives are applied, discussed and checked for plausibility on two clearly defined loading conditions for the internal deformation energy and single point displacements on different locations. [ABSTRACT FROM AUTHOR]

Mechanical metamaterials are most often assemblies of stocky beam elements connected through rigid connections, hinges, or flexural joints. The description of these materials through classical beam theories is challenging because of the wide variety of complex phenomena observed in the severe deformation regime mechanical metamaterials must undergo and because most classical beam theories can only be applied to elements with sufficiently high slenderness. In the spirit of Hencky, Turco et al. (2020) has recently formulated an intrinsically discrete nonlinear elastic model suitable for the design of mechanical metamaterials. The objective of this contribution was to present a numerical study of the nonlinear generalization of the Timoshenko beam that results from the asymptotic homogenization of the discrete model introduced by Turco et al. The present numerical study took into account several loading cases and elucidated the sensitivity of the homogenized continuum with respect to axial, bending, and shear stiffness parameters, as well as to load imperfections, in terms of mechanical behavior, including buckling onset and post-critical behavior. It was found that the predictions obtained with the homogenized model in the large deformation regime matched excellently with those of the discrete model proposed by Turco et al. [ABSTRACT FROM AUTHOR]

The piezocone (CPTu) dissipation test is used to characterize how the applied load from the penetrating cone is distributed between the soil and pore fluid during both penetrometer advancement and when penetration is paused. The coefficient of consolidation is often estimated from CPTu dissipation tests by interpreting the rate of excess porewater pressure (Au) decay to static conditions during a pause in cone penetration. Most CPTu dissipation test interpretation methods are based on Terzaghi consolidation theory for Au dissipation at the cone shoulder (u2 position) or cone face (u1 position) and assume that radial Au dissipation dominates the response. However, several recent studies show that vertical Au migration does contribute to the response. This study uses a large deformation direct axisymmetric cone penetration model to characterize the soil-water mechanical response during CPTu dissipation tests, and in particular, the role of vertical Au dissipation on the response at the u1 and u2 positions. Large deformations around the penetrating cone are accommodated with an Arbitrary Lagrangian Eulerian approach. Soil behavior is modeled with the MIT-S1 constitutive model calibrated for Boston blue clay (BBC) soil behavior. Au dissipation following undrained cone penetration is simulated with coupled consolidation for BBC with over-consolidation ratios (OCR) of 1, 2, and 4 and a range of hydraulic conductivity anisotropy. The simulated u1 and u2 dissipation responses are presented to study how they are affected by OCR and hydraulic conductivity anisotropy. A correction factor is recommended to account for hydraulic conductivity anisotropy when interpreting the horizontal coefficient of consolidation from CPTu dissipation tests. [ABSTRACT FROM AUTHOR]

The coupled Eulerian–Lagrangian (CEL) method implemented in Abaqus is an established tool for modelling large deformations in numerical geomechanics. As shown in previous work, it can be extended to a hydro‐mechanically coupled scheme by exploiting the similarity of the heat balance equation to the mass balance equation of fluids. However, the distinction between effective and total contact stresses has not been possible in this approach, which hinders its application to problems with interface friction as frictional stresses are calculated based on total normal contact stress. An approach to circumvent this problem is presented in this work. Its relevance is demonstrated by the simulation of vibratory pile driving model tests in water‐saturated sand. The implementation by means of user‐subroutines is available and works for any total‐stress analysis. [ABSTRACT FROM AUTHOR]

Engineering structures may undergo large deformations, but simulating is still challenging for existing numerical methods, for example, the element‐based methods struggle from the mesh distortion and the strong form particle‐based methods exhibit tensile instability. This article aims on presenting a novel numerical method for large deformation simulations, which is named the implicit Updated Lagrangian Fragile Points Method (ULFPM). The point‐based nature of the proposed method ensures immunity to mesh distortion, and its stability is guaranteed by its foundation on weak form formulations. For verifications, the proposed implicit ULFPM has been applied to several large deformation problems. For all the examples, the proposed method is able to provide reliable results with a good agreement with the reference results. Moreover, the implicit ULFPM performs better than the Finite Element Method to some extent for extremely large deformation problems. It is also discussed that the accuracy of the implicit ULFPM is improved significantly by using the support domain refinement scheme. The examples indicate that the proposed method can serve as a reliable tool for predicting the large deformations of structures in engineering practices. [ABSTRACT FROM AUTHOR]

The material point method (MPM) has been widely used in the simulation of large deformation problems involving hydromechanical coupling recently. Here, an explicit stabilized formulation of hydromechanically coupled two-phase MPM with zero air pressure for both saturated and unsaturated conditions is presented, and to avoid numerical instability when low-order MPM is applied to hydromechanically coupled problems, techniques including low-order shape functions based on the Hu-Washizu multi-field variational principle, the B-bar matrix, and the reduced integration are implemented in the algorithm of MPM. The accuracy of the formulation is verified through numerical examples involving the consolidation problem and Liakopoulos drainage test, and then, two cases, the unsaturated slope failure under rainfall infiltration as well as the Yanyuan landslide, are performed. The simulation results further demonstrate the capability of the present formulation to capture the hydromechanical behavior as well as the failure and post-failure stages when modelling hydromechanical large deformation problems. [ABSTRACT FROM AUTHOR]

Large deformations of soft rocks often occur during the excavation and support of the Chuxiong section tunnel in the Yunnan Central Diversion Project. The physical characteristics and creep mechanical properties of the red-bed soft rock were analyzed by combining engineering experience, laboratory tests, and scanning electron microscopy. Furthermore, the creep parameters of the red-bed soft rock were obtained. The issues related to large deformations of deeply buried tunnels with soft and weak rock masses were investigated. Based on construction engineering practice and numerical simulations, characteristics of extrusion damage of deeply buried tunnels with soft and weak rock masses were analyzed. Countermeasures were implemented to solve the problems of large deformations, which can be used as references for the construction of similar soft rock tunnels in the future. [ABSTRACT FROM AUTHOR]

Coated superconducting radio-frequency (SRF) cavities are planned to be implemented in the Future Circular Collider (FCC) at the European Organization for Nuclear Research (CERN). The interest in industrialized and high-performance processes for fabrication of the corresponding copper substrates has thus risen. Tubular hydroforming is a well-known industrial process, but has not been thoroughly applied for ultra-pure oxygen-free electronic copper (Cu-OFE) thick products. To provide a feasibility analysis for the optimized fabrication process of copper substrate seamless cavities, a Forming Limit Diagram (FLD) of the material of interest was studied. In this paper, the methodology, test results and initial benchmark of the material model is presented, for 4 mm and 2 mm thick sheets.

The piezocone (CPTu) dissipation test is used to characterize how the applied load from the penetrating cone is distributed between the soil and pore fluid during both penetrometer advancement and when penetration is paused. The coefficient of consolidation is often estimated from CPTu dissipation tests by interpreting the rate of excess porewater pressure (∆u) decay to static conditions during a pause in cone penetration. Most CPTu dissipation test interpretation methods are based on Terzaghi consolidation theory for ∆u dissipation at the cone shoulder (u2 position) or cone face (u1 position) and assume that radial ∆u dissipation dominates the response. However, several recent studies show that vertical ∆u migration does contribute to the response. This study uses a large deformation direct axisymmetric cone penetration model to characterize the soil-water mechanical response during CPTu dissipation tests, and in particular, the role of vertical ∆u dissipation on the response at the u1 and u2 positions. Large deformations around the penetrating cone are accommodated with an Arbitrary Lagrangian Eulerian approach. Soil behavior is modeled with the MIT-S1 constitutive model calibrated for Boston blue clay (BBC) soil behavior. ∆u dissipation following undrained cone penetration is simulated with coupled consolidation for BBC with over-consolidation ratios (OCR) of 1, 2, and 4 and a range of hydraulic conductivity anisotropy. The simulated u1 and u2 dissipation responses are presented to study how they are affected by OCR and hydraulic conductivity anisotropy. A correction factor is recommended to account for hydraulic conductivity anisotropy when interpreting the horizontal coefficient of consolidation from CPTu dissipation tests.

The features of thin-film membranes, which are formed above round holes in silicon substrates using the Bosch-process are considered. The membrane has a complex shape due to the presence of the stress state of the initial films. The analysis of the dependence of the membrane deflection w on the supplied overpressure P is used to calculate the mechanical characteristics of the membranes. In this case, it is necessary to determine directly on the membrane its diameter, the thickness of the constituent layers, the change in the topography of the membrane surface over its entire area as the overpressure increases. Determination of the membrane diameter and the thicknesses of the constituent layers is shown by the example of p-Si*/SiNx/SiO2 and SiNx/SiO2/SiNx/SiO2 membranes. We used spectral ellipsometry, energy-dispersive X-ray spectroscopy, optical profilometry, optical microscopy. The influence of the peculiarities of the fixing conditions on the stress-strain state of membranes is shown, and the assessment is carried out by means of numerical modeling. A technique has been developed for measuring and calculating the mechanical characteristics of membranes that have an initial deflection. The calculation result is shown on the example of a membrane with an initial deflection of 2 µm—SiNx/SiO2/SiNx/SiO2 and a membrane with an initial deflection of 30 µm—Al/SiO2/Al. [ABSTRACT FROM AUTHOR]

This chapter discusses the use of the surface calorimetry approach to study rubber deformation. It introduces the theoretical framework for determining heat source (or heat power density) from full temperature field measurements and the heat diffusion equation. The determination of the mean intrinsic dissipation and the strain-induced crystallinity from the heat sources is presented and discussed. Typical results obtained under homogeneous tensile loadings are reviewed and analyzed according to four types of calorimetric responses. The types of responses depend on whether the rubber is filled or not, and whether it is crystallizing or not. The calorimetric signatures of thermo-elasticity, viscosity, strain-induced crystallization, stress softening, and energy storage are analyzed and discussed. [ABSTRACT FROM AUTHOR]

We propose a new Cahn–Hilliard phase field model coupled to incompressible viscoelasticity at large strains, obtained from a diffuse interface mixture model and formulated in the Eulerian configuration. A new kind of diffusive regularization, of Allen–Cahn type, is introduced in the transport equation for the deformation gradient, together with a regularizing interface term depending on the gradient of the deformation gradient in the free energy density of the system. The designed regularization preserves the dissipative structure of the equations. We obtain the global existence of a weak solution in three space dimensions and for generic nonlinear elastic energy densities with polynomial growth, comprising the relevant cases of polyconvex Mooney–Rivlin and Ogden elastic energies. Also, our analysis considers elastic free energy densities which depend on the phase field variable and which can possibly degenerate for some values of the phase field variable. We also propose two kinds of unconditionally energy stable finite element approximations of the model, based on convex splitting ideas and on the use of a scalar auxiliary variable respectively, proving the existence and stability of discrete solutions. We finally report numerical results for different test cases with shape memory alloy type free energy, showing the interplay between phase separation and finite elasticity in determining the topology of stationary states with pure phases characterized by different elastic properties. [ABSTRACT FROM AUTHOR]

Locking effects can be a major concern during the numerical modelling of elastic materials, especially for large strains. Those effects arise from volumetric constraints such as incompressibility or anisotropic effects of the underlying material class. One particular solution strategy is to employ mixed formulations, which provide solutions tailored to the specific locking phenomena at hand. While being in general powerful, one drawback of such solution strategies is that the provided strategy to overcome locking is often tied or limited to some specific topological type of finite elements and thus forfeiting generality. Contrary the Virtual Element Method (VEM) benefits by definition from allowing arbitrary element shapes and number of nodes at element level. A variety of approaches for the treatment of locking phenomena for hyperelastic material is formulated in this contribution for the Virtual Element Method with a low order ansatz. Key ingredient to the implementation of multi-field mixed principles in VEM is the consideration of only one constant variable per field and one corresponding Lagrange multiplier over the entire virtual element. Hereby the stabilization contribution utilizes the mixed formulation but shares the element-wise constant variable with the projection part of the virtual element. A direct consequence of this rather simple implementation strategy is the combination of powerful mixed formulations with a computational approach that is able to treat general element shapes. The proposed formulations are tested with regard to structured mesh at standard examples in computational mechanics as well as at specific computational engineering applications where also unstructured meshes are utilized. [ABSTRACT FROM AUTHOR]

With the use of a mathematical model of large deformations of materials with elastic, plastic, and viscous properties, an analytical solution was obtained for deformation under creep conditions of a plug in a round tube with a varying pressure drop. The motion is considered taking into account the sliding of the material in the vicinity of the rigid wall of the pipe and its deformation under increasing, constant, and decreasing pressure. The displacements, reversible and irreversible deformations, and stresses at all stages of deformation, including residual deformations and stresses at full unloading, are calculated. [ABSTRACT FROM AUTHOR]

The results of calculations of the stress-strain states of an elastoplastic material containing a single cylindrical continuity defect and loaded with external pressure are presented. The hydrostatic pressure on the surface distant from the defect initially increases, remains constant for some time and then gradually decreases to zero. The process of comprehensive compression leaves, after unloading, a formed level and distribution of residual stresses in the vicinity of the continuity defect. The change in such stresses is calculated upon repeated loading and unloading. Intensity and nature of repeated loads are considered identical to the original ones. Calculations are carried out within the framework of the stated one-dimensional problem of the theory of large deformations. The material is assumed to be incompressible. The development of areas of viscoplastic flow in the active part of the process and their attenuation during unloading are taken into account. Changes in the geometric dimensions of the evolving defect are assessed. [ABSTRACT FROM AUTHOR]

The article presents an approximate (semianalytical) solution of the one-dimensional nonstationary problem of the thermal conductivity of a uniformly deforming plate (shell) under time-dependent boundary conditions of the third kind, obtained using the proposed piecewise integral heat balance method. It is shown that a change in the thickness of the plate (shell) on deformation affects not only the quantitative, but also the qualitative behavior of temperature and heat flux at different points of the plate. It has been established that with an increase in the frequency of temperature fluctuations on the inner surface of the plate, thermal disturbances penetrate into the plate to a shorter distance. [ABSTRACT FROM AUTHOR]

In order to establish the dynamic equations of the rigid-flexible coupled robotic mechanisms with large beam-deformations over the horizontal plane, a thorough modeling technique founded on the virtual work concept has been proposed. Based on the transformed full-actuated model, the predefined-time robust sliding mode control strategy is developed to track the prescribed angular positions of the rigid-flexible coupled robotic mechanisms. In addition to compensating the time-varying external disturbances, the nonlinear disturbance observer is also integrated and resolved into predefined-time robust sliding mode schemes. By introducing the virtual input, the robust linear quadratic state feedback controller is developed to eliminate the tracking errors and vibration modes of the rigid-flexible coupled robotic mechanisms simultaneously. Furthermore, it is proved that the tracking errors and vibration modes can be uniformly stable under the developed scheme based on Lyapunov's stability theory. Finally, three numerical examples are conducted to access the effectiveness and excellence of the presented nonlinear disturbance observer-based predefined-time robust sliding mode and robust linear quadratic state feedback strategies in comparison to nonlinear disturbance observer-based backstepping control and slide mode control schemes. [ABSTRACT FROM AUTHOR]

In this work, the task was to investigate the processes of microstructure change occurring in relatively large bulk bars under the action of large plastic deformations. Such large levels of deformation are usually achievable in high pressure twisting of small flat disks, but are difficult to achieve in large bulk bars. The method of radial shear rolling makes it possible to achieve comparable ultrahigh degrees of deformation (~45 mm/mm) in combination with the vortex flow of the metal. Sequential rolling of the E110 zirconium alloy was carried out under extreme conditions on 2 radial shear rolling mills with a total diameter reduction ε = 185 % and a maximum accumulated strain = 46 mm/mm. To assess the level of deformation and its distribution over the section, FEM modeling was carried out in Deform‑3D. The resulting structure was studied by electron microscopy (TEM/SEM). A detailed cross‑sectional study of the EBSD structure was performed with a resolution of 1 mm. A gradient structure with a predominance of an equiaxed ultrafine‑grained structure was found, which was not very pronounced compared to the use of smaller deformations.

Based on more than three decades of rod finite element theory, this publication combines the successful contributions found in the literature and eradicates the arising drawbacks like loss of objectivity, locking, path‐dependence and redundant coordinates. Specifically, the idea of interpolating the nodal orientations using relative rotation vectors, proposed by Crisfield and Jelenić in 1999, is extended to the interpolation of nodal Euclidean transformation matrices with the aid of relative twists; a strategy that arises from the SE(3)$$ SE(3) $$‐structure of the Cosserat rod kinematics. Applying a Petrov–Galerkin projection method, we propose a rod finite element formulation where the virtual displacements and rotations as well as the translational and angular velocities are interpolated instead of using the consistent variations and time‐derivatives of the introduced interpolation formula. Properties such as the intrinsic absence of locking, preservation of objectivity after discretization and parameterization in terms of a minimal number of nodal unknowns are demonstrated by representative numerical examples in both statics and dynamics. [ABSTRACT FROM AUTHOR]

This article serves as a continuation of our previously published work and focuses on loose material transport via sandwich belt conveyors. Experimental, analytical, stochastic, and numerical approaches are used to obtain and utilize the moduli of a bilateral Winkler elastic foundation that represent a loose material, which is wheat (Triticum aestivum) that is free of bran in this case. The solutions were obtained for a uniformly and nonuniformly distributed loose material. The task of the conveyor with loose material is simplified into a symmetric task, i.e., a beam on an elastic bilateral Winkler foundation, for an analytical solution and stochastic solution (Anthill and Matlab sw). In a numerical approach, this is considered a plane strain problem within the finite element method (Ansys and MSC.Marc sw). The experimental data are evaluated and used to obtain the functions of Winkler elastic foundation moduli, which are further considered in the numerical solution. The finite element method mainly serves as a verification tool. The acquired histograms of the elastic foundation moduli can be further applied in various scientific and research fields. [ABSTRACT FROM AUTHOR]