Finite element formulations for large deformation dynamic analysis

Abstract Starting from continuum mechanics principles, finite element incremental formulations for non‐linear static and dynamic analysis are reviewed and derived. The aim in this paper is a consistent summary, comparison, and evaluation of the formulations which have been implemented in the search for the most effective procedure. The general formulations include large displacements, large strains and material non‐linearities. For specific static and dynamic analyses in this paper, elastic, hyperelastic (rubber‐like) and hypoelastic elastic‐plastic materials are considered. The numerical solution of the continuum mechanics equations is achieved using isoparametric finite element discretization. The specific matrices which need be calculated in the formulations are presented and discussed. To demonstrate the applicability and the important differences in the formulations, the solution of static and dynamic problems involving large displacements and large strains are presented.