ALE stress update for transient and quasistatic processes

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 re ect the relative motion between the nite 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 signi cant extra computational cost. These ideas are illustrated by means of two numerical examples