Arbitrary Lagrangian-Eulerian (ALE) formulation for hyperelastoplasticity

Author (s): Rodríguez-Ferran, A., Pérez-Foguet, A. and Huerta, A.
Journal: International Journal for Numerical Methods in Engineering

Volume: 53, Issue 8
Pages: 1831 – 1851
Date: 2002



The Arbitrary Lagrangian-Eulerian (ALE) description in nonlinear 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 is required in the description of the elastic response. This is not
the case in previous formulations, were 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..



@article {2002-IJNME-RPH,
author = {Rodr\'iguez-Ferran, A.,  P\'erez-Foguet, A. and Huerta, A.},
title = {Arbitrary Lagrangian–Eulerian (ALE) formulation for hyperelastoplasticity},
journal = {International Journal for Numerical Methods in Engineering},
volume = {53},
number = {8},
pages = {1831--1851},
year = {2002},
url = {},
doi = {10.1002/nme.362},