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Recently, numerous studies have demonstrated that the physics-informed neural network (PINN) can effectively and accurately resolve hyperelastic finite deformation problems. In this paper, a PINN framework for tackling hyperelastic-magnetic coupling problems is proposed. Since the solution space consists of two-phase domains, two separate networks are constructed to independently predict the solution for each phase region. In addition, a conscious point allocation strategy is incorporated to enhance the prediction precision of the PINN in regions characterized by sharp gradients. With the developed framework, the magnetic fields and deformation fields of magnetorheological elastomers (MREs) are solved under the control of hyperelastic-magnetic coupling equations. Illustrative examples are provided and contrasted with the reference results to validate the predictive accuracy of the proposed framework. Moreover, the advantages of the proposed framework in solving hyperelastic-magnetic coupling problems are validated, particularly in handling small data sets, as well as its ability in swiftly and precisely forecasting magnetostrictive motion. [ABSTRACT FROM AUTHOR]

In this article, a nonlinear geometrically exact (GeX) hybrid-mixed four-node solid-shell element under non-conservative loading using the sampling surfaces (SaS) method is developed. The term "geometrically exact" means that the parametrization of the middle surface is known and, therefore, the coefficients of the first and second fundamental forms and the Christoffel symbols are taken exactly at element nodes. The SaS formulation is based on the choice of N SaS parallel to the middle surface and located at Chebyshev polynomial nodes in order to introduce the displacements of these surfaces as fundamental shell unknowns. Such a choice of unknowns with the use of Lagrange polynomials of degree N–1 in the through-thickness distributions of displacements, strains, and stresses leads to an efficient higher-order shell formulation. To develop the hybrid-mixed four-node solid-shell element, which is free of shear and membrane locking, the Hu–Washizu variational principle is utilized. The proposed GeX hybrid-mixed solid-shell element subjected to follower loads shows superior performance in the case of coarse meshes and allows the use of only one load step in most of the considered numerical examples. It is established that the difference between the second Piola-Kirchhoff and Cauchy stresses in some non-conservative problems for isotropic and composite shells undergoing finite rotations can be significant. [ABSTRACT FROM AUTHOR]

We investigate finite plane deformations of an elliptic rigid inclusion embedded in a soft matrix that is made of a particular class of harmonic-type hyperelastic materials. The inclusion is assumed to be perfectly bonded to the matrix, which is subjected to a constant remote in-plane loading. Utilizing the Cauchy integral techniques associated with conformal mappings, we derive closed-form solutions for the full-field deformation, Piola stress, and Cauchy stress in the entire matrix. Numerical examples are presented to illustrate the current solutions in comparison with those established from linear elasticity theory. We find that in terms of the Cauchy stress around the inclusion, the maximum normal stress component always appears at the endpoints of the major axis of the inclusion, irrespective of the magnitude of the remote loading, while the maximum hoop stress component occurs not exactly at the above-mentioned endpoints when the remote loading exceeds a certain value. In particular, we identify an exact explicit formula for determining the relative rotation of the inclusion during deformation induced by a remote uniaxial loading of arbitrarily given magnitude and direction. [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]

This study focuses on investigating hard-magnetic soft materials, characterized by magnetoactive polymers containing magnetically polarized particles as fillers. The research utilizes the Gent model of hyperelasticity to analyze the propagation of Lamb waves in a magnetically induced deformed compressible plate. In this investigation, we explore both finite deformations and incremental wave propagation in nonlinear hard-magnetic soft materials. The main objective is to formulate the elastic tensor and relevant wave equations within the framework of Lagrangian space. To assess the dispersion characteristics of the guided wave, the study introduces and discusses an extension of the semi-analytical finite element (SAFE) method. Using this numerical approach, the research further examines the effects of magnetic flux densities and its orientation with respect to wave propagation direction on the dispersion characteristics of the fundamental Lamb modes. The study starts by examining the limiting case of the neo-Hookean material model to explain such inherent dependencies. These dependencies are then further emphasized by including the strain-stiffening effect that the Gent material model describes. The research findings reveal the presence of a threshold applied magnetic flux, beyond which the Gent-type material may undergo a snap-through instability, resulting in changes in the dispersion characteristics of the fundamental symmetric Lamb mode. [ABSTRACT FROM AUTHOR]

• Phase field fracture model capable of finite deformation simulation for flexible piezoelectric. • The coupled governing equations are solved via SPSA and RCSA-EO strategies. • Can predict the fracture behavior of flexible piezoelectrics under electromechanical environments. Fracture failure is a major concern in mechanical engineering, particularly for piezoelectric materials. In contrast to other numerical methods, phase field method has significant advantages in addressing fracture progress. It can automatically track crack surfaces through ordered parameter evolution, which is versatile for modeling complex fracture behaviors. However, previous studies on phase field fracture in piezoelectric solids have primarily focused on brittle ceramics with small deformation. In recent years, flexible piezoelectrics with high stretchability have already been achieved in industrial production. These materials exhibit obvious nonlinear characteristics during deformation, which renders the traditional assumption of small deformations inadequate for predicting their fracture behaviors. In this work, we propose a finite deformation phase field fracture model for flexible piezoelectric materials, building upon the established nonlinear electromechanical material model. The numerical framework is carried out in the commercial software ABAQUS via a user element subroutine. Both single–pass staggered algorithm (SPSA) and residual-controlled staggered algorithm with even-odd iteration split (RCSA-EO) are employed to solve coupled electro-mechanical-phase field governing equations. The proposed model is validated through comparisons with analytical solutions and existing literature. Moreover, the developed numerical framework effectively explains the nonlinear fracture behavior observed in experiments conducted on Polyvinylidene fluoride (PVDF), a flexible piezoelectric material with a large failure strain. Numerical simulations are also performed to demonstrate the influence of the applied electric field on electromechanical fracture behavior. The results highlight that the specific impact of electric fields depends on material parameters, geometric parameters, and boundary conditions. The developed model is capable of making accurate and realistic predictions of fracture in flexible piezoelectric materials. This is particularly important for evaluating the reliability and safety of flexible piezoelectric devices. [ABSTRACT FROM AUTHOR]

The contribution at hand aims to numerically simulate the nail driving process using the finite element method. The geometrical constraint of the impenetrability between the surfaces of the two contacting bodies is delivered using a displacement-driven approach. The Coulomb friction law is employed to describe the interaction between two contacting surfaces, where the coefficient of friction is obtained experimentally. In this work, the driving of a nail into blocks of polyurethane (PUR) and spruce wood is simulated in a quasi-static manner. Von Mises plasticity is employed to model PUR, while a more complicated constitutive model is utilized for spruce wood. This constitutive formulation considers the influence of the grain direction as well as the nonlinear behavior of spruce wood. The driving forces obtained from the numerical simulation are compared to the experiments. Despite simplifications and assumptions, the comparison demonstrates reasonable agreement in the simulation of nailing into PUR. Under the same circumstances, the comparison in the case of spruce wood shows a more reasonable agreement at the initial stages but fails prematurely due to severe mesh distortion. Overlooking the distortion issue, which must be further investigated, the outcome demonstrates the stability and reliability of the material and contact model. [ABSTRACT FROM AUTHOR]

This study finds the mode I crack tip quantities for plastically compressible hardening solids exposed to fluctuating loading whereas the same for plastically incompressible solids has also been done for comparative analysis. The assumptions like small scale yielding and plane strain have been made for the present analysis. The effects of load ratio, stress intensity factor range, and plastic compressibility on the crack tip deformation and fields have been reported. A quick convergence of cyclic paths of crack-tip-opening-displacement is observed to stabilize self-similar loops in case of positive load ratio and lower load range. However, the same type of convergence pattern is not observed for higher load range and zero load ratio. Time taken for the stabilization of those self-similar loops is increased with increase in the plastic compressibility. The load range, load ratio and compressibility affect the growth of crack notably. [ABSTRACT FROM AUTHOR]

A continuum mechanical model of coupled dislocation based plasticity and fracture at finite deformation is proposed. Motivating questions and target applications of the model are sketched. [ABSTRACT FROM AUTHOR]

In this research, we present a gradient theory of poroelasticity based on the couple-stress. Within the context of finite deformations and in a thermodynamically consistent manner, the constitutive equations for the porous solid are derived by including the solid vorticity gradient and its power-conjugate counterpart, namely, the couple-stress. Subsequently, a linearized theory for an isotropic porous solid is developed in which two microstructure-dependent constitutive moduli (or equivalently, two material length-scale parameters) are introduced. To investigate the gradient effects on the responses of the material, the problem of wave propagation in fluid-saturated porous solids is formulated and solved based on the proposed theory. For comparison, the wave dispersion and attenuation curves are compared with those obtained from classical theory of poroelasticity. [ABSTRACT FROM AUTHOR]

Magnetoelasticity theories describe the behavior of solids in response to the application of a magnetic field. This paper presents a new thermodynamically consistent constitutive theory for simulating nonlinear responses of solids for which the strain energy density depends on the deformation gradient through the Biot strain tensor and specializes the theory for application to the problem of finite deformation of a circular cylindrical tube. The derived theory appears to be attractive for applications as it provides a relatively simple mathematical expression for modeling nonlinear magneto-mechanical responses of solids. For the considered problem, it is obtained that a higher modified pressure is required to maintain a specified azimuthal stretch when a magnetic field is applied. Finally, and among other things, it is observed that the influence of the magnetic field can either decline or progressively enhance with increasing azimuthal stretch. [ABSTRACT FROM AUTHOR]

Modeling of constitutive theory of smart materials is an intensely researched topic in mechanics of solids. This is due to its complexity and widespread applications. This article presents general constitutive theory for dielectric semilinear materials and specializes the theory for applications to problems of extension-inflation coupling and radial deformation of electro-sensitive tubes based on prototype energy function of John's semilinear material. During extension-inflation coupling of an incompressible tube, it is obtained that a lower pressure is required to maintain a prescribed azimuthal stretch when an electric field is applied. Finally, and among other things, the numerical solutions of the considered problems coincide with those predicted by the Dorfmann and Ogden theory. [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 (∆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.

Fracture of materials with rate-dependent mechanical behaviour, e.g. polymers, is a highly complex process. For an adequate modelling, the coupling between rate-dependent stiffness, dissipative mechanisms present in the bulk material and crack driving force has to be accounted for in an appropriate manner. In addition, the resistance against crack propagation can depend on rate of deformation. In this contribution, an energetic phase-field model of rate-dependent fracture at finite deformation is presented. For the deformation of the bulk material, a formulation of finite viscoelasticity is adopted with strain energy densities of Ogden type assumed. The unified formulation allows to study different expressions for the fracture driving force. Furthermore, a possibly rate-dependent toughness is incorporated. The model is calibrated using experimental results from the literature for an elastomer and predictions are qualitatively and quantitatively validated against experimental data. Predictive capabilities of the model are studied for monotonic loads as well as creep fracture. Symmetrical and asymmetrical crack patterns are discussed and the influence of a dissipative fracture driving force contribution is analysed. It is shown that, different from ductile fracture of metals, such a driving force is not required for an adequate simulation of experimentally observable crack paths and is not favourable for the description of failure in viscoelastic rubbery polymers. Furthermore, the influence of a rate-dependent toughness is discussed by means of a numerical study. From a phenomenological point of view, it is demonstrated that rate-dependency of resistance against crack propagation can be an essential ingredient for the model when specific effects such as rate-dependent brittle-to-ductile transitions shall be described. [ABSTRACT FROM AUTHOR]

Next-generation lithium-ion batteries with silicon anodes have positive characteristics due to higher energy densities compared to state-of-the-art graphite anodes. However, the large volume expansion of silicon anodes can cause high mechanical stresses, especially if the battery active particle cannot expand freely. In this article, a thermodynamically consistent continuum model for coupling chemical and mechanical effects of electrode particles is extended by a change in the boundary condition for the displacement via a variational inequality. This switch represents a limited enlargement of the particle swelling or shrinking due to lithium intercalation or deintercalation in the host material, respectively. For inequality constraints as boundary condition a smaller time step size is need as well as a locally finer mesh. The combination of a primal-dual active set algorithm, interpreted as semismooth Newton method, and a spatial and temporal adaptive algorithm allows the efficient numerical investigation based on a finite element method. Using the example of silicon, the chemical and mechanical behavior of one- and two-dimensional representative geometries for a charge-discharge cycle is investigated. Furthermore, the efficiency of the adaptive algorithm is demonstrated. It turns out that the size of the gap has a significant influence on the maximal stress value and the slope of the increase. Especially in two space dimensions, the obstacle can cause an additional region with a lithium-poor phase. [ABSTRACT FROM AUTHOR]

A morphing flap, a morphing wing section, can deform its geometrical shape seamlessly and continuously to improve the aerodynamic performance. To obtain a compliant morphing flap internal mechanism to realize the target deformation, this study aimed to develop a nonlinear topology optimization method based on a level-set method. However, numerical instability occurs during the design optimization process within the scope of finite deformation analyses. Accordingly, the numerical instability problem caused by an artificial weak material representing a void region in the optimization algorithm was resolved. In particular, this problem was resolved by structural modeling without such weak materials using the mesh adaptation method and by installing a spring component with a negligibly small spring constant. Subsequently, a finite deformation analysis was performed and integrated with the level-set-based topology optimization model. Finally, the proposed method was validated by solving the morphing flap design problem through numerical analyses, wherein an optimum structural configuration under finite deformation was obtained. [ABSTRACT FROM AUTHOR]

Dielectric elastomers (DEs) are a class of electro-active polymers (EAPs) that can deform under electric stimuli and have great application potential in bionic robots, biomedical devices, energy harvesters, and many other areas due to their outstanding deformation abilities. It has been found that stretching rate, temperature, and electric field have significant effects on the stress-strain relations of DEs, which may result in the failure of DEs in their applications. Thus, this paper aims to develop a thermo-electro-viscoelastic model for DEs at finite deformation and simulate the highly nonlinear stress-strain relations of DEs under various thermo-electro-mechanical loading conditions. To do so, a thermodynamically consistent continuum theoretical framework is developed for thermo-electro-mechanically coupling problems, and then specific constitutive equations are given to describe the thermo-electro-viscoelastic behaviors of DEs. Furthermore, the present model is fitted with the experimental data of VHB4905 to determine a temperature-dependent function of the equilibrium modulus. A comparison of the nonlinear loading-unloading curves between the model prediction and the experimental data of VHB4905 at various thermo-electro-mechanical loading conditions verifies the present model and shows its ability to simulate the thermo-electro-viscoelastic behaviors of DEs. Simultaneously, the results reveal the softening phenomena and the instant pre-stretch induced by temperature and the electric field, respectively. This work is conducive to analyzing the failure of DEs in functionalities and structures from theoretical aspects at various thermo-electro-mechanical conditions. [ABSTRACT FROM AUTHOR]

Tissue failure and damage are inherent parts of vascular diseases and tightly linked to clinical events. Additionally, experimental set-ups designed to study classical engineering materials are suboptimal in the exploration of vessel wall fracture properties. The classical Compact Tension (CT) test was augmented to enable stable fracture propagation, resulting in the symmetry-constraint Compact Tension (symconCT) test, a suitable set-up for fracture testing of vascular tissue. The test was combined with Digital Image Correlation (DIC) to study tissue fracture in 45 porcine aorta specimens. Test specimens were loaded in axial and circumferential directions in a physiological solution at 37 ° C. Loading the aortic vessel wall in the axial direction resulted in mode I tissue failure and a fracture path aligned with the circumferential vessel direction. Circumferential loading resulted in mode I-dominated failure with multiple deflections of the fracture path. The aorta ruptured at a principal Green-Lagrange strain of approximately 0.7, and strain rate peaks that develop ahead of the crack tip reached nearly 400 times the strain rate on average over the test specimen. It required approximately 70% more external work to fracture the aorta by circumferential than axial load; normalised with the fracture surface, similar energy levels are, however, observed. The symconCT test resulted in a stable fracture propagation, which, combined with DIC, provided a set-up for the in-depth analysis of vascular tissue failure. The high strain rates ahead of the crack tip indicate the significance of rate effects in the constitutive description of vascular tissue fracture. This paper represents a significant step forward in understanding the fracture properties of porcine aorta. Inspired by the Compact Tension test, we developed an ad hoc experimental protocol to investigate stable crack propagation in soft materials, providing new insights into the mechanical processes that lead to the rupture of vascular tissue. The set-up enables the assessment of strains and strain rates ahead of the crack tip, and our findings could improve the clinical risk assessment of vascular pathologies as well as optimise medical device design. [Display omitted] [ABSTRACT FROM AUTHOR]

Having accurate data to represent hyperelastic materials that underpin soft robotics would facilitate their analysis, design, and validation. We seek to provide the reader with a useful tool to overcome a mundane but crucially important problem in determining the hyperelastic material properties. We show how to employ first dimensionless and then dimensional comparisons between experimental data and the classic theoretical model representing this system to produce C1 and C2 for the Mooney-Rivlin model, closely representing a variety of soft polymers.

This paper presents an analytical and numerical study of the homogenization problem of suspensions of vacuous bubbles in viscoelastic rubber subject to finite quasistatic deformations. The focus is on the elementary case of bubbles that are initially equiaxed in shape and isotropically distributed in space and on isotropic incompressible rubber with Gaussian elasticity and constant viscosity. From an analytical point of view, asymptotic solutions are worked out in the limits: i ) of small deformations, i i ) of finite deformations that are applied either infinitesimally slowly or infinitely fast, and i i i ) when the rubber loses its ability to store elastic energy and reduces to a Newtonian fluid. From a numerical point of view, making use of a recently developed scheme based on a conforming Crouzeix-Raviart finite-element discretization of space and a high-order accurate explicit Runge-Kutta discretization of time, sample solutions are worked out for suspensions of initially spherical bubbles of the same (monodisperse) size under a variety of loading conditions. Consistent with a recent conjecture of Ghosh et al. (J. Mech. Phys. Solids 155:104544, 2021), the various asymptotic and numerical solutions indicate that the viscoelastic response of the suspensions features the same type of short-range-memory behavior — in contrast with the generally expected long-range-memory behavior — as that of the underlying rubber, with the distinctive differences that their effective elasticity is compressible and their effective viscosity is compressible and nonlinear. By the same token, the various solutions reveal a simple yet accurate analytical approximation for the macroscopic viscoelastic response of the suspensions under arbitrary finite quasistatic deformations. [ABSTRACT FROM AUTHOR]

Developing appropriate analytic-function-based constitutive models for new materials with nonlinear mechanical behavior is demanding. For such kinds of materials, it is more challenging to realize the integrated design from the collection of the material experiment under the classical topology optimization framework based on constitutive models. The present work proposes a mechanistic-based data-driven topology optimization (DDTO) framework for three-dimensional continuum structures under finite deformation. In the DDTO framework, with the help of neural networks and explicit topology optimization method, the optimal design of the three-dimensional continuum structures under finite deformation is implemented only using the uniaxial and equi-biaxial experimental data. Numerical examples illustrate the effectiveness of the data-driven topology optimization approach, which paves the way for the optimal design of continuum structures composed of novel materials without available constitutive relations. [ABSTRACT FROM AUTHOR]

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A rational study has been made to describe the behavior of anisotropic granular materials by a hypoplastic constitutive equation. The concept of the microstructure tensor in describing the anisotropy has been implemented to develop a general form of a hypoplastic constitutive equation for anisotropic materials. Attempt was made to present all formulations in a rational way with no additional assumption. Both inherent and induced anisotropy have been studied and the evolution of the material internal structure has been rationally defined through an evolutionary function. Since all developments are primarily mathematical, no particular form of a constitutive equation has been assumed. Verifications by some available experimental data reveal the success of the proposed developments outlined in this study. [ABSTRACT FROM AUTHOR]

This paper introduces a coupled electromechanical finite deformation phase field model for crack propagation and interfacial decohesion in multiphase piezoelectric composites with interfaces. The crack phase field model is augmented with cohesive traction-separation laws at the material interfaces, derived from a cohesive potential function. A Gibbs free energy density function is proposed, allowing for the incorporation of the anisotropic elastic stiffness of the piezoelectric material. Numerical simulations exhibiting different failure mechanisms are carried out to demonstrate the efficacy of the model. Effects of external electric field on crack evolution and the competition between penetration and deflection of a crack impinging on an interface are investigated. Limited verification tests are conducted with theoretical results. Finally, the model is used to simulate fracture in nonuniform piezocomposite microstructures. The effect of crack propagation on the evolution of the electric field with different crack face conditions are analyzed. Differences in the electromechanical responses of piezocomposites due to different fiber distributions are also observed. [ABSTRACT FROM AUTHOR]

In this paper, we study the stress concentration around a circular rigid inclusion in an incompressible anisotropic homogeneous nonlinearly elastic thin sheet subjected to in-plane finite deformation uniaxial extension. Two classes of material symmetry are considered: transverse isotropy and orthotropy. For the case of transverse isotropy, a three-parameter constitutive relation that under infinitesimal deformations reduces appropriately to the classical incompressible linearized elastic transversely isotropic constitutive relation is studied. Similarly, a six-parameter constitutive relation is considered for the case of orthotropic material symmetry. These constitutive relations may be suitable to describe the response of transversely isotropic and orthotropic bodies subjected to moderate deformations. [ABSTRACT FROM AUTHOR]

The internally balanced material theory, which can be viewed as a generalization of hyperelasticity, is extended to treat material swelling. Swelling problems involving eventual contact with fixed rigid surfaces are considered, first for a situation where the post-contact deformation is homogeneous, and then for a situation where the post-contact deformation is not homogeneous. The latter requires the solution of a boundary value problem in the internally balanced material setting. Both situations are considered in detail for a neo-Hookean-like constitutive specification in the internally balanced material framework. [ABSTRACT FROM AUTHOR]

A generic smeared crack modeling framework predicated on the deformation gradient decomposition (DGD) approach is proposed for use in dynamic fracture problems at finite strains, accommodating failure along multiple mutually orthogonal fracture planes embedded within an independently defined bulk material model. Within this constitutive framework, the traction equilibrium conditions imposed at each failure surface are used to determine the associated crack displacements stored as internal state variables. In general, the enforcement of interfacial equilibrium entails the implicit solution of a non-linear system of equations within the constitutive update procedure. However, if inertial effects arising due to the relative motion of the fractured material are incorporated within the model, the traction equilibrium conditions are shown to give rise to corresponding dynamic equations of motion governing the time-evolution of the crack opening displacements. For dynamic problems, an explicit time-integration procedure is devised to efficiently update the material state, subject to a set of internal frictionless contact constraints to prevent material inversion. The efficacy of the proposed modeling framework is investigated through several benchmark dynamic fracture problems run within the explicit finite element code DYNA3D. [ABSTRACT FROM AUTHOR]

This work extends the recent US‐ATFH8 element to 3D hyper‐elastic finite deformation analysis. Using two sets of shape functions, the new 3D element comprises of 8 nodes and 24 DOFs. The first set of shape functions represent the test functions that come from the conventional isoparametric interpolation, and the second set, representing the trial functions, are constructed from the homogenous solutions for linear elasticity governing equations, termed analytical trial functions (ATFs). This study considers finite deformation for hyper‐elastic materials, but it is assumed that the analytical solutions associated with hyper‐elastic materials can be updated to hold approximately in each incremental step. Moreover, the deformation information required for stress computation is updated by using the incremental deformation gradient, which is constructed from the updated ATFs. Numerical examples show that without additional pressure DOF, the element US‐ATFH8 still behaves well in nearly incompressible hyper‐elastic 3D problems with finite deformation, even when the meshes are extremely distorted. [ABSTRACT FROM AUTHOR]

Variation of cyclic loading effect on fatigue crack growth is investigated under plane strain and small scale yielding (SSY) conditions. The material is characterized by a finite strain elastic viscoplastic constitutive model with hardening and hardening-softening-hardening hardness functions. Displacements corresponding to the isotropic linear elastic mode I crack field are prescribed on a remote boundary. The influence of cyclic stress intensity factor range ( Δ K), load ratio (R), number of cycles (N), plastic compressibility ( α) , overload and material softening on near tip deformation was studied in detail. For comparison purpose, a few results pertaining to plastically incompressible solids are also considered. The crack tip opening displacement (CTOD), plastic crack growth, deformed crack tip shape, plastic zone shape and size near the crack tip appear to depend significantly on Δ K , R, N, α , overload and material softening. The overload produces strong plastic deformation ahead of the crack tip and decreases the fatigue crack growth substantially. Variation of cyclic loading effect on fatigue crack growth is investigated for materials characterized by a finite strain elastic viscoplastic constitutive model with hardening and hardening-softening-hardening hardness functions. Both plastically compressible and incompressible solids are considered. The influence of cyclic stress intensity factor range ( Δ K), load ratio (R), number of cycles (N), plastic compressibility ( α) , overload and material softening on near tip deformation was studied in detail. The crack tip opening displacement, plastic crack growth, plastic zone shape and size near the crack tip appear to depend significantly on Δ K , R, N, α , overload and material softening. The combination of softening or softening-hardening material response and plastic compressibility leads to major deviations in crack tip blunting and fatigue crack growth from those that prevail for a hardening material. [ABSTRACT FROM AUTHOR]

The constitutive models of shape memory hydrogels (SMHs) are gaining increasing interest due to their important applications in human tissue, artificial skin, and drug release because these models can elucidate the interaction between water molecule diffusion and transient network deformation, and clarify the mechanism of shape memory effect. Herein, based on the chain statistic theory, a micro-macroscopic SMH constitutive model is developed, which simultaneously considers solvent diffusion and network evolution. Compared with existing models, our model considers the coupling effect of water molecule diffusion and dynamic network deformation, kinetics of dynamic bond controlled by temperature, chemical potential and chain force, and can capture the location-dependent shape memory effect of SMHs. In addition, this model is implemented into ABAQUS through a user material subroutine (UMAT) and the simulation results are in reasonable agreement with experimental measurements. Three simulation examples, the constrained swelling of a strip, deformation of a flat plate with a hole and SMH indentation, are presented and simulation results indicate that our model can capture the location-dependent shape memory behaviors. This work provides a powerful tool to elucidate complex mechanical behaviors of SMHs and may guide their structure designs and applications. [Display omitted] • Feature of coupled water molecule diffusion and dynamic network deformation. • Performance of location-dependent shape memory effect in shape memory hydrogels. • Kinetics of dynamic bonds controlled by temperature-chemical potential-chain force. [ABSTRACT FROM AUTHOR]

The present paper studies the stress-strain state of a round reinforced with stiffeners plate of elastic-plastic material carried out of a refined theory of the type by S.P. Timoshenko It is believed that plate vibrations are excited by a pulsed load. The relationship between displacement and deformation is assumed to be geometrically non-linear. The plate consists of sheathing and rib reinforcement of a quadrangular cross section. The lining materials of the reinforcing ribs are considered identical and obeying Hooke's law. The cross sections of the ribs are constant and are independent of the radial coordinate. The height of the ribs and their locations are set using a single column function. The number of methods of finite differences the solution to the problem. In this case, deformations, forces, moments, and transverse forces are determined at the centers of the grid elements, and displacement and rotation angles are determined at the grid nodes. Given the location of the ribs, the deflection of the central point and the force calculated, depend on the radial co-ordinate and time. Particularly, it was found that the smallest deflection of the central point is achieved when the rib is located in the middle of the radius of the plate; the location of the ribs near the edge of the plate can lead to a decrease in the load-bearing capacity of the structure compared to an un-reinforced plate.

In our earlier work, we formulated the Schwarz alternating method as a means for concurrent multiscale coupling in finite deformation solid mechanics for quasi‐static problems. Herein, we advance this method for the study of transient dynamic multiscale solid mechanics problems where information is exchanged back and forth between small and large scales. The extension to dynamics relies on the notion of a global time stepper. Within each global time step, the subdomains are coupled by the standard Schwarz iterative process. Remarkably, each subdomain can use its own time step or even its own time integrator to advance its solution in time, provided that they synchronize at each global time step. We study the performance of the Schwarz method on several examples designed for this purpose. Our numerical experiments demonstrate that the method is capable of coupling regions with different mesh resolutions, different element types, and different time integration schemes (e.g., implicit and explicit), all without introducing any artifacts that afflict other coupling methods for transient dynamics. Finally, we apply the dynamic Schwarz alternating method to the simulation of a bolted joint subjected to dynamic loading, as a demonstration of the performance of the method in a realistic scenario. [ABSTRACT FROM AUTHOR]

Sliding connections are present in several applications on the mechanics, civil and aerospace industries. A framework consisting on an accurate and stable formulation to describe the dynamics of flexible systems with sliding connections is developed. The total Lagrangian positional approach of the Finite Element Method is employed using 2D solid and frame elements to discretize bodies and connections. This allows a wide range of applications, particularly the local modelling of joints. The proposed formulation includes roughness along sliding paths independent from the finite element geometry discretization. Following variational principles, Lagrange multipliers are used to impose sliding constraints on the equations of motion. A direct time integration is performed by the generalized-a method and its stability in the present finite deformation context is evaluated. The resulting nonlinear equations are solved by the Newton-Raphson method. Examples are presented where the proposed framework is evaluated regarding its dynamical behavior and to solve practical scenarios for which sliding modelling is a necessity. [ABSTRACT FROM AUTHOR]

The peridynamics is a new meshless method, which has developed rapidly in recent years because of its superiority in dealing with discontinuity problems. In this paper, we established elastoplastic constitutive relations of finite deformation using Jaumann stress rate, Almansi strain rate, von Mises yield criteria, associated flow and isotropic hardening rule under the framework of non-ordinary state-based peridynamics. Further, the updated Lagrange solution method to the constitutive relation has also been proposed. We applied the solution to simulate the large elastoplastic tensile deformation of a rod and necking of a cylindrical bar, and the results are consistent with the analytical solution and the experimental results, separately. Our findings prove that the theory and method proposed in this paper are applicable to the analysis of elastoplastic finite deformation. [ABSTRACT FROM AUTHOR]

We develop a mathematical model that builds on the surprising nonlinear mechanical response observed in recent experiments on nematic liquid crystal elastomers. Namely, under uniaxial tensile loads, the material, rather than thinning in the perpendicular directions, becomes thicker in one direction for a sufficiently large strain, while its volume remains unchanged. Motivated by this unusual large-strain auxetic behaviour, we model the material using an Ogden-type strain-energy function and calibrate its parameters to available datasets. We show that Ogden strain-energy functions are particularly suitable for modelling nematic elastomers because of their mathematical simplicity and their clear formulation in terms of the principal stretches, which have a direct kinematic interpretation. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'. [ABSTRACT FROM AUTHOR]

Biological composites can overcome the conflict between strength and toughness to achieve unprecedented mechanical properties in engineering materials. The suture joint, as a kind of heterogeneous architecture widely existing in biological tissues, is crucial to connect dissimilar components and to attain a tradeoff of all-sided functional performances. Therefore, the suture joints have attracted many researchers to theoretically investigate their mechanical response. However, most of the previous models focus on the sutural interface between two chemically similar stiff phases with (or without) a thin adhesive layer, which are under the framework of linear elasticity and small deformation. Here, a general model based on the finite deformation framework is proposed to explore the stiffness and toughness of chemically dissimilar suture joints connecting soft and stiff phases. Uniaxial tension tests are conducted to investigate the tensile response of the suture joints, and finite element simulations are implemented to explore the underlying mechanisms, considering both material nonlinearity and cohesive properties of the interface. Two failure modes are quantitively captured by our model. The stored elastic energy in the soft phase competes with the energy dissipation due to the interface debonding, which controls the transition among different failure modes. The toughness of the suture joints depends on not only the intrinsic strengths of the constituent materials and their cohesive strength, but also the interfacial geometry. This work provides the structure-property relationships of the soft/stiff suture joints and gives a foundational guidance of mechanical design towards high-performance bioinspired composites. [ABSTRACT FROM AUTHOR]

A well known result from the non-linear theory of elasticity applied to spherical shells is that the classical Mooney-Rivlin constitutive law may give either a monotonic or a non-monotonic pressure-inflation response for finite deformation. Specifically, this is determined by two factors: the relative shell thickness, and the relative I 1 to I 2 contribution in the M-R constitutive law. Here we consider how a residual stress field may affect this behavior. Using a constitutive framework for hyperelastic materials with residual stress that has been especially applied to tubes, this paper focuses on finite thickness spherical shells while using a similar prototypical energy response. In this context we examine different residual stress states, and show how certain of these lead to more workable analytical results than others. All of them enable Taylor and asymptotic expansions in the small and large inflation limit. On this basis it is shown how particular residual stress fields can cause a monotonic inflation graph to become non-monotonic, and vice versa. [ABSTRACT FROM AUTHOR]