Development and Application of an ALE Large Deformation Formulation

This paper presents a complete derivation and implementation of the Arbitrary Lagrangian Eulerian (ALE) formulation for the simulation of nonlinear static and dynamic problems in solid mechanics. While most of the previous work done on ALE for dynamic applications was mainly based on operator split and explicit calculations, this work derives the quasi-static and dynamic ALE equations in its simple and correct form, using a fully coupled implicit approach. Full expression for the ALE virtual work equations is given. Time integration relations for the dynamic equations are also derived. Examples of quasi-static and dynamic large deformation applications are presented.