Large Elastoplastic Deformations Research Articles

Nonstationary Axisymmetric Elastic Processes in an Incompressible Medium with Preliminary Finite Irreversible Deformations

The kinematic equations of the multiplicative model of large elastoplastic deformations are generalized for hardening materials with different principal directions of the stress and plastic strain rate tensors. By taking into account the intermediate configuration, an algorithm is proposed for analyzing dynamic elastic processes in a medium with preliminary irreversible deformations. The use of the algorithm is illustrated by the example of cylindrical elastic shock waves in an incompressible elastoplastic medium.

Large deformation in bi-material components by XIGA and coupled FE-IGA techniques

In the recent years, isogeometric analysis (IGA) has found wide application in modeling different types of discontinuities produced by cracks, contact surfaces and bi-material interfaces. This technique eliminates the geometry discretization errors associated with the representation of complex geometries. The present paper employs the extended isogeometric analysis (XIGA) and the coupled finite element-isogeometric analysis (FE-IGA) to model large elasto-plastic deformations in bi-material engineering components. XIGA models all types of discontinuities independent of the grid chosen for analysis. Instead, the standard displacement-based approximation is enriched with additional enrichment functions to include the effects of these discontinuities in the formulation. In the coupled FE-IGA technique, IGA is used in the weak portion of the domain to eliminate the problems of mesh distortion and conventional finite element method is used in the stronger portion where mesh distortions do not occur. The transition elements are employed to couple the finite element and isogeometric portions of the domain. Finally, several numerical problems are solved by XIGA and coupled FE-IGA techniques to illustrate the applicability, efficiency and accuracy of the proposed techniques in modeling large elasto-plastic deformations in bi-material specimens. The results obtained in the present study are compared with finite element solutions which have been taken as the reference solution for the given problems.

On instability of constitutive models for isotropic elastic-perfectly plastic material behaviour at finite deformations

The main goal of this work is to test the possibility of a newly introduced constitutive law to model the behaviour of the isotropic elastic-perfectly plastic material which is exposed to large elastoplastic deformations. The proposed constitutive relation is based on the hypo-elastic relation and the inelastic INTERATOM model. The verification of the model is done by its implementation into the commercial software ABAQUS/Standard via the user subroutine UMAT. For that purpose, the large simple shear problem is studied where selected objective corotational rates, i.e. the logarithmic rate, the Jaumann rate and the Green-Naghdi rate, are individually implemented in the aforementioned constitutive relations. The obtained results are compared mutually and with the relevant literature. The proposed constitutive model is also used to test the behaviour of the part of a real engineering structure, i.e. a seismic isolator, in order to obtain the correct input data for further analysis of superstructure behaviour due to seismic excitation.

Elasto-plastic large deformation analysis of multi-patch thin shells by isogeometric approach

This paper studies elasto-plastic large deformation behaviour of thin shell structures using the isogeometric computational approach with the main focus on the efficiency in modelling the multi-patches and arbitrary material formulation. In terms of modelling, we employ the bending strip method to connect the patches in the structure. The incorporation of bending strips allows to eliminate the strict demand of the C1 continuity condition, which is postulated in the Kirchhoff-Love theory for thin shell, and therefore it enables us to use the standard multi-patch structure even with C0 continuity along the patch boundaries. Furthermore, arbitrary nonlinear material models such as hyperelasticity and finite strain plasticity are embedded in the shell formulation, from which a unified thin shell formulation can be achieved. In terms of analysis, the Bézier decomposition concept is used to retain the local support of the traditional finite element. The performance of the presented approach is verified through several numerical benchmarks.

Elasto-plastic large deformation analysis of bi-material components by FEM

This paper presents the modeling of large elasto-plastic deformations in bi-material engineering components by employing the conventional finite element method (FEM). The updated Lagrangian Approach has been used to take into account the large deformations occurring in the domain. The Von-Mises yield criterion with isotropic hardening has been used to model the elasto-plastic behaviour of the material. Bilinear and multilinear plasticity models have been used to model the plastic behaviour of the material. Finally, several numerical problems are solved using FEM to demonstrate the applicability of this method in the modeling and simulation of large deformation phenomenon in bi-material components.

Mathematical modeling of creep and viscoplastic flow of a cylindrical layer material

Within the framework of a mathematical model of large elastoplastic deformations, taking into account viscous properties of materials, a boundary value problem of creep and viscoplastic flow of a material in the gap between two rigid coaxial cylindrical surfaces under rectilinear motion of the inner surface is considered. Irreversible deformations accumulate from the beginning of the deformation process and are initially associated with the creep process of the material, which is described using the Norton creep power law. With a subsequent increase in the speed of movement of the inner cylinder at some time point, the stress state will reach the yield surface and a viscoplastic flow will begin in the material. As a plastic potential, we use the Tresca yield criterion, generalized in the case of taking into account the viscous properties of the material. The viscoelastic deformation, the emergence and development of the viscoplastic flow under uniformly accelerated motion of the inner surface, the flow under constant speed, and the flow inhibition under equal slow motion of the surface to a full stop are considered. Stresses, reversible and irreversible deformations, displacements are calculated, stress relaxation after the complete stop of the cylinder is investigated.

On the use of domain-based material point methods for problems involving large distortion

Challenging solid mechanics problems exist in areas such as geotechnical and biomedical engineering which require numerical methods that can cope with very large deformations, both stretches and torsion. One candidate for these problems is the Material Point Method (MPM), and to deal with stability issues the standard form of the MPM has been developed into new domain-based techniques which change how information is mapped between the computational mesh and the material points. The latest of these developments are the Convected Particle Domain Interpolation (CPDI) approaches. When these are demonstrated, they are typically tested on problems involving large stretch but little torsion and if these MPMs are to be useful for the challenging problems mentioned above, it is important that their capabilities and shortcomings are clear. Here we present a study of the behaviour of some of these MPMs for modelling problems involving large elasto-plastic deformation including distortion. This is carried out in a unified implicit quasi-static computational framework and finds that domain distortion with the CPDI2 approaches affects some solutions and there is a particular issue with one approach. The older CPDI1 approach and the standard MPM however produce physically realistic results. The primary aim of this paper is to raise awareness of the capabilities or otherwise of these domain-based MPMs.

CD-MPM

We present two new approaches for animating dynamic fracture involving large elastoplastic deformation. In contrast to traditional mesh-based techniques, where sharp discontinuity is introduced to split the continuum at crack surfaces, our methods are based on Continuum Damage Mechanics (CDM) with a variational energy-based formulation for crack evolution. Our first approach formulates the resulting dynamic material damage evolution with a Ginzburg-Landau type phase-field equation and discretizes it with the Material Point Method (MPM), resulting in a coupled momentum/damage solver rooted in phase field fracture: PFF-MPM. Although our PFF-MPM approach achieves convincing fracture with or without plasticity, we also introduce a return mapping algorithm that can be analytically solved for a wide range of general non-associated plasticity models, achieving more than two times speedup over traditional iterative approaches. To demonstrate the efficacy of the algorithm, we also develop a Non-Associated Cam-Clay (NACC) plasticity model with a novel fracture-friendly hardening scheme. Our NACC plasticity paired with traditional MPM composes a second approach to dynamic fracture, as it produces a breadth of organic, brittle material fracture effects on its own. Though NACC and PFF can be combined, we focus on exploring their material effects separately. Both methods can be easily integrated into any existing MPM solver, enabling the simulation of various fracturing materials with extremely high visual fidelity while requiring little additional computational overhead.

Dynamics of Unloading and Elastic Waves in a Medium with Accumulated Plastic Pre-Deformations

Approaches that allow one to describe the elastic dynamics of a medium (including unloading and elastic loading) in the presence of irreversible pre-deformations are proposed for a model of large elastoplastic deformations. Formulas based on a rotation tensor are obtained for calculating the redistribution of plastic strains. For dynamic elastic processes generating shock waves in an elastoplastic medium, the possible rates and types of plane shock waves are determined. It is shown that elastic shock waves create jumps in the field of plastic pre-deformations. Relations for calculating such discontinuities are obtained. The main properties of modeling self-similar solutions taking into account the proposed approach to the description of the kinematics of the medium and the possibility of distinguishing between elastic and plastic strains are considered.

Hierarchical hexachiral auxetics for large elasto-plastic deformation

To improve the auxeticity and isotropy behavior of standard hexachiral structures at large elasto-plastic deformation, the authors have earlier proposed a modified hexachiral structure with wavy ligaments (Zhu et al 2018 Smart Material Structures 27 055001). While a significant improvement was achieved with the proposed modified chiral structure, it was reported therewith that its auxeticity and isotropy degrade rapidly at large tensile deformation, in contrast to the excellent performance in compression. The present work builds upon the basic structure proposed in (Zhu et al 2018 Smart Material Structures 27 055001), to further improve the mechanical behavior in tension, without compromising the already excellent performance achieved at large compressive deformation. To reduce the distortion of the central ring in a hexachiral structure—the deformation mechanism that degrades its mechanical performance in tension—a hierarchical hexachiral structure is proposed, where a standard hexachiral structure reinforces the central ring of the basic hexachiral structure in (Zhu et al 2018 Smart Material Structures 27 055001). A significant improvement in mechanical behavior over the basic structure is demonstrated, with potential applications in a protective system.

Theoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticity

The aim of this paper is to compare a hyperelastic with a hypoelastic model describing the Eulerian dynamics of solids in the context of non-linear elastoplastic deformations. Specifically, we consider the well-known hypoelastic Wilkins model, which is compared against a hyperelastic model based on the work of Godunov and Romenski. First, we discuss some general conceptual differences of the two approaches. Second, a detailed study of both models is proposed, where differences are made evident at the aid of deriving a hypoelastic-type model corresponding to the hyperelastic model and a particular equation of state used in this paper. Third, using the same high order ADER Finite Volume and Discontinuous Galerkin methods on fixed and moving unstructured meshes for both models, a wide range of numerical benchmark test problems has been solved. The numerical solutions obtained for the two different models are directly compared with each other. For small elastic deformations, the two models produce very similar solutions that are close to each other. However, if large elastic or elastoplastic deformations occur, the solutions present larger differences.

A Meshless Method Based on the Nonsingular Weight Functions for Elastoplastic Large Deformation Problems

In this study, based on a nonsingular weight function, the improved element-free Galerkin (IEFG) method is presented for solving elastoplastic large deformation problems. By using the improved interpolating moving least-squares (IMLS) method to form the approximation function, and using Galerkin weak form based on total Lagrange formulation of elastoplastic large deformation problems to form the discretilized equations, which is solved with the Newton–Raphson iteration method, we obtain the formulae of the IEFG method for elastoplastic large deformation problems. In numerical examples, the influences of the penalty factor, scale parameter of influence domain and weight functions on the computational accuracy are analyzed, and the numerical solutions show that the IEFG method for elastoplastic large deformation problems has higher computational efficiency and accuracy.

Some Properties of Elastic Dynamics of a Medium with Preliminary Large Irreversible Deformations

The nonstationary dynamics of a medium without additional accumulation of plastic strains over preexisting ones is considered in the framework of a model of large elastoplastic deformations. For such a case, it is shown that the velocities and types of arising elastic shock waves completely repeat the wave pattern for a nonlinearly-elasticmedium, whereas the compatibility conditions for discontinuities do not depend on the plastic strains. Some general formulas for calculating the rotation and redistribution of plastic deformations are obtained. The results are illustrated by relatively simple example with the plane one-dimensional shock waves. For an isotropic nonlinear relation between the stresses and elastic strains, it is shown that the plane elastic shock waves are divided into quasi-longitudinal, quasi-transverse, and rotational ones. It is also shown that, in the general case, some jump rotation of plastic deformations can occur on each of the elastic waves.

Finite-Element Simulations of Elastoplastic Flow during Compression of a Sample in a Diamond Anvil Cell under Extremely High Pressure: Effects of Geometry and Material Properties

Extreme pressures of several megabars are produced during compression of sample and gasket within a diamond anvil cell. This study uses finite-element simulations to analyze the effects of culet geometry, bevel angle, sample thickness, and the sample-gasket system. Multiple experimental phenomena are reproduced and interpreted. These results improve our understanding of material mechanical response under extreme pressure and large elastoplastic deformation, to benefit optimal design of the diamond anvil cells that are key to high-pressure research, and thus the search for and study of $e.g.$ metallic hydrogen.

Mathematical modeling of dynamic stability of shell structures under large elastoplastic deformations

In this paper, a mathematical model of dynamic stability of a ring plate under the action of large elastoplastic strains is considered. Such problems are encountered in pressing, for example, by a pulse magnetic field, of ring plates supported on the inner contour. The obtained results show that the proposed mathematical model agrees well with experimental data.

Auxetic hexachiral structures with wavy ligaments for large elasto-plastic deformation

The hexachiral structure is in-plane isotropic in small deformation. When subjected to large elasto-plastic deformation, however, the hexachiral structure tends to lose its auxeticity and/or isotropy—properties which are desirable in many potential applications. The objective of this study is to improve these two mechanical properties, without significantly compromising the effective yield stress, in the regime with significant material and geometrical nonlinearity effects. It is found that the deformation mechanisms underlying the auxeticity and isotropy properties of a hexachiral structure are largely influenced by the extent of rotation of the central ring in a unit cell. To facilitate the development of this deformation mechanism, an improved design with wavy ligaments is proposed. The improved performance of the proposed hexachiral structure is demonstrated. An initial study on possible applications as a protective material is next carried out, where the improved hexachiral design is shown to exhibit higher specific energy absorption capacity compared to the original design, as well as standard honeycomb structures.

Logarithmic rate implementation in constitutive relations of finite elastoplasticity with kinematic hardening

AbstractThe objective of this article is the evaluation of the validity range of two objective rates, the nowadays most frequently used Jaumann rate and the recently introduced logarithmic rate, in material behaviour prediction due to large deformations. For that purpose the model subjected to large monotonic uniaxial elastoplastic deformation has been examined as well as the initially prestressed models which are afterwards exposed to the cyclic process of combined elastic lengthening and shearing. It is shown that whenever the participation of shear deformation to the total deformation stays in the small deformation range both rates are almost equal in constitutive relations implementation since the outputs for both rates are nearly congruent. Otherwise, if the influence of rotations is significant the Jaumann rate gives theoretically and experimentally unexpected results whereas the logarithmic rate results are stable and consistent with the notion of elasticity, i.e. without any residual stresses at the end of the elastic deformation cycles.

Deformation and Heating of an Elastoviscoplastic Cylindrical Layer Moving Owing to a Varying Pressure Drop

Within the framework of the theory of large elastoplastic deformations generalized to the case of viscous and thermophysical properties of materials, we give a solution of a sequence of coupled problems on the onset and development of a flow in a material layer filling the gap between two rigid coaxial cylindrical surfaces under increasing pressure drop and on the subsequent flow deceleration under decreasing pressure gradient. Here the thermophysical and deformation processes are coupled, and the yield stress depends on temperature. Heat production due to the layer material friction against the rough cylindrical boundary surfaces is taken for an additional heat source.

Large Elasto-Plastic Deformations in Bi-Material Components by Coupled FE-EFGM

In the recent years, the coupled finite element-element free Galerkin method (coupled FE-EFGM) has found wide application in modeling large elasto-plastic deformations in bi-material components. The coupled FE-EFGM applies EFGM in the portion of the domain where large deformations are expected to occur, whereas the rest of the domain is discretized into conventional finite elements. The large deformation occurring in the domain has been modeled by using the total Lagrangian approach. The non-linear elasto-plastic behavior of the material has been represented by the Ramberg-Osgood model. Finally, two numerical problems are solved by the coupled FE-EFGM to illustrate its applicability, efficiency and accuracy in modeling large elasto-plastic deformations in bi-material samples.

A Reaction-Diffusion Phase-Field Model and Its Application to Lithiated Selenium-Doped Germanium Electrodes

Recent experiments observed micrometer (µm)-sized Selenium (Se)-doped Germanium (Ge) particles forms a network of active Ge inclusions amidst an amorphous Se-containing inactive phase during initial lithiation/delithiation cycles. Such an inactive coating phase is supposed to be responsible for the superior performance of cycling stability and capacity over un-doped Ge particles of similar size, however, the understanding of fundamental mechanism still remain elusive. A reaction-diffusion phase-field model, coupling the large elastoplastic deformation, is therefore originally developed investigate the role of the inactive phase in morphology and stress variation of Se-doped Ge electrode upon lithiation. The incorporation of both the Butler-Volmer electrochemical reaction kinetics and Li diffusion, for the first time, enables to directly determine the conditions at which the lithiation process exhibits the diffusion and/or reaction controlled behavior. We find that the hoop stress at the surface of Ge particles is significantly suppressed by the protection of the inactive coating phase, especially when characterized by the soft nature and the high Li diffusivity. The present study reveals the physical underpinnings of previously unexplained favorable electrochemical reaction, diffusion and fracture behavior of active/inactive-phase anodes, and thus offers valuable insights and guidance toward high-performance anodes for lithium-ion batteries.