Arbitrary Lagrangian–Eulerian (ALE) formulation for hyperelastoplasticity

Abstract

The arbitrary Lagrangian–Eulerian (ALE) description in non-linear solid mechanics is nowadays stan- dard 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 e>ects, and a convection phase, where the relative motion between the material and the ?nite element mesh is considered. In contrast to previous ALE formulations of hyperelasticity or hyperelastoplasticity, the deformed con?guration at the beginning of the time-step, not the initial undeformed con?guration, is chosen as the reference con?g- uration. As a consequence, convecting variables are required in the description of the elastic response. This is not thecasein previous formulations, whereonly theplastic responsecontains 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 tes