Abstract

A key issue in Arbitrary Lagrangian-Eulerian (ALE) non-linear solid mechanics is the correct treatment of the convection terms in the constitutive equation. These convection terms, which reflect the relative motion between the finite element mesh and the material, are found for both transient and quasistatic ALE analyses. It is shown in this paper that the same explicit algorithms can be employed to handle the convection terms of the constitutive equation for both types of analyses. The most attractive consequence of this fact is that a quasistatic simulation can be upgraded from Updated Lagrangian (UL) to ALE without significant extra computational cost. These ideas are illustrated by means of two numerical examples.

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.