Recent trends in ALE formulation and its applications in solid mechanics Original Research Article

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. The ALE equations are presented using a fully coupled implicit approach. Full expression for the ALE virtual work equations and finite element matrices are given. The matrix equations are presented in a level of details that facilitates straightforward implementation. Time integration relations for the dynamic equations are also derived. Special techniques are presented to adapt the formulation for simulating crack propagation problems. Several applications in the areas of metal forming, metal cutting and crack propagation are solved and presented.