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

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.