Splitting Time Integrator for Transient Analysis of Nearly Incompressible Elasticity

Abstract

Since the velocity of the P-wave may be much larger than that of the S-wave in nearly incompressible materials, explicit time integrators are hardly applied to such problems. This paper presents a novel time integration scheme for transient finite element analysis of nearly incompressible elasticity. The proposed time integrator is derived by extending the Rattle algorithm for constrained Hamiltonian systems. The proposed approach works as an implicit scheme for the P-wave propagation while it works as an explicit one for the S-wave. Thus its numerical stability depends on only the Swave velocity.