A novel semi-implicit scheme for elastodynamics and wave propagation in nearly and truly incompressible solids

Abstract This paper presents a novel semi-implicit scheme for elastodynamics and wave propagation problems in nearly truly incompressible material models. The proposed methodology is based on the efficient computation of Schur complement mixed displacement-pressure formulation using lumped mass matrix displacement field. By treating deviatoric stress explicitly pressure field implicitly, critical time step made to be limited by shear speed rather than bulk speed. convergence demonstrated computing error norms recently LBB-stable BT2/BT1 element. Using numerical examples modelled with Neo-Hookean Ogden models, it that yields significant computational benefits over fully explicit implicit schemes finite strain simulations involving materials. Finally, applicability models illustrated.