Abstract

In this work we compare two frameworks for thermodynamically consistent hyperelasto-plasticity with kinematic hardening. The first was formulated by Dettmer and Reese (2004), inspired by Lion (2000), and has been used to model sheet metal forming. The second, formulated by Wallin et al. (2003), has been used to model large shear strains and cyclic ratcheting behavior of pearlitic steel (Johansson et al. 2006). In this paper we show that these frameworks can result in equivalent models for certain choices of free energies. Furthermore, it is shown that the choices of free energy found in the literature only result in minor differences. These differences are discussed theoretically and investigated numerically.

Abstract

In this paper, a new strategy for the simulation of quasi-static cold compaction processes of powders is presented. A material model formulated within the framework of isotropic finite strain multiplicative hyperelastoplasticity is used. An elliptic plastic model expressed in terms of the Kirchhoff stresses and the relative density models the transition between the loose powder and the compacted sample. The Coulomb dry friction model is used to capture friction effects at powder-die contact. Excessive distortion of Lagrangian meshes due to large mass fluxes is usual in powder compaction problems. Moreover, Lagrangian approaches cannot deal properly with mass fluxes around sharp corners. For these reasons, an Arbitrary Lagrangian-Eulerian (ALE) formulation is used here. The present results illustrate that this approach allows simulating highly demanding powder compaction processes without mesh distortion and spurious oscillations in the results. Moreover, it is shown that the mass conservation principle is verified with a low relative error.

Abstract

The arbitrary Lagrangian–Eulerian (ALE) description in non‐linear solid mechanics is nowadays standard for hypoelastic–plastic models. An extension to hyperelastic–plastic models is presented here. A fractional‐step method—a common choice in ALE analysis—is employed for time‐marching: every time‐step is split into a Lagrangian phase, which accounts for material effects, and a convection phase, where the relative motion between the material and the finite element mesh is considered. In contrast to previous ALE formulations of hyperelasticity or hyperelastoplasticity, the deformed configuration at the beginning of the time‐step, not the initial undeformed configuration, is chosen as the reference configuration. As a consequence, convecting variables are required in the description of the elastic response. This is not the case in previous formulations, where only the plastic response contains convection terms. In exchange for the extra convective terms, however, the proposed ALE approach has a major advantage: only the quality of the mesh in the spatial domain must be ensured by the ALE remeshing strategy; in previous formulations, it is also necessary to keep the distortion of the mesh in the material domain under control. Thus, the full potential of the ALE description as an adaptive technique can be exploited here. These aspects are illustrated in detail by means of three numerical examples: a necking test, a coining test and a powder compaction test.

Abstract

The paper considers an overview of the problems of mathematical modeling of geomechanical processes occurring in rocks during the geological exploration and development of reservoirs and well boring process. The mathematical formulation is based on the theory of repeated superposition of large deformations. A numerical discretization of the posed boundary problems of interacting solids is performed using a discontinuous spectral element method and multi-point constraints at non-matching mesh interfaces between interacting solid rock structures. Several industrial applications of the developed approach are considered. Seismic wave propagation in the heterogeneous media with initial geomechanical stresses is considered. A modelling of an induced anisotropy is performed by the superposition of dynamic deformations onto initial generally finite strains. Use of variable order spectral elements at non-conformal meshes allows one to simplify the process of unstructured mesh generation for the discretization of complex geological models and to set the local spatial order of the SEM discretization depending on the speed of seismic waves in geological structures, which significantly reduces the computational costs when conducting numerical modeling and lowers the requirements to the model preprocessing and mesh quality. The considered approach allows predicting in more detail the behavior of the rock during reservoir development, taking into account different stages of the field deformations. In particular, the redistribution of accumulated deformations during multistep loading and / or changes in the structure (topology) of the loaded body, as well as contact conditions of adhesion / sliding at the interlayer boundaries and bonded contacts are taken into account. These problems were solved using CAE Fidesys software, which allows solving static and dynamic problems of geomechanics and geophysics using finite (FEM) and spectral (SEM) element methods of a variable approximation order in space at non-conformal unstructured meshes.

Abstract

A material model to deal with finite plasticity coupled with anisotropic damage will be presented. The presentation addresses mesh regularization problems and a novel approach for using gradient-extension in the context of damage. Since finite strains are considered, the strain measures chosen are logarithmic strains. To give the interested audience an idea of the behavior of the model, numerical examples are used for illustration.

Abstract

Within this contribution, we discuss additional theoretical as well as numerical aspects of the material model developed in [1, 2], where a `two-surface' damage-plasticity model is proposed accounting for induced damage anisotropy by means of a second order damage tensor. The constitutive framework is stated in terms of logarithmic strain measures, while the total strain is additively decomposed into elastic and plastic parts. Moreover, a novel gradientextension based on the damage tensor's invariants is presented using the micromorphic approach introduced in [3]. Finally, going beyond the numerical examples presented in [1, 2], we study the model's ability to cure mesh-dependency in a three-dimensional setup.

Abstract

Thermoplastic materials are widely used for thermoforming and injection moulding processes, since their low density in combination with a high strength to mass ratio are interesting for various industrial applications. Semi-crystalline polymers make up a subcategory of thermoplastics, which partly crystallize after cool-down from the molten state. During the thermoforming process, residual stresses can arise, due to complex material behavior under different temperatures and strain rates. Therefore, computational models are needed to predict the material response and minimize production errors. This work presents a thermomechanically consistent phenomenological material formulation at finite strains, based on [1]. In order to account for the highly nonlinear material behavior, elasto-plastic and visco-elastic contributions are combined in the model formulation. To account for the crystalline regions, a hyperelastic-plastic framework is chosen, based on [2, 3]. Kinematic hardening of Arruda-Boyce form is incorporated in the formulation, as well as associated plastic flow. The material parameters depend on both, the temperature as well as the degree of crystallinity. A comparison to experiments with varying degrees of crystallinity and temperatures is presented, where a special blending technique ensures stable crystallinity conditions.