Exact energy and momentum conserving algorithms for general models in nonlinear elasticity

Abstract

Implicit time integration schemes that inherit the conservation laws of total energy, linear and angular momentum are considered for initial boundary-value problems in finite-deformation elastodynamics. Conserving schemes are constructed for general hyperelastic material models, both compressible and incompressible, and are formulated in a way that is independent of spatial discretization. Three numerical examples for Ogden-type material models, implemented using a finite element discretization in space, are given to illustrate the performance of the proposed schemes. These examples show that, relative to the standard implicit mid-point rule, the conserving schemes exhibit superior numerical stability properties without a compromise in accuracy.