Lax-Wendroff schemes for elastic-plastic solids

Thomas Heuzé (1)

1 GeM - Institut de Recherche en Génie Civil et Mécanique

Two formulations of the Lax-Wendroff scheme are proposed in this paper for its extension to elastic-plastic solids. The unknown vector consists of the strain or stress components in addition to the velocity ones according to the chosen formulation. The Lax-Wendroff scheme is here implemented in its Richtmyer two-step version so that the projection of the elastic trial stresses onto the yield locus is performed twice per time step. It is shown that it allows to reduce the number of cells required for the approximation of discontinuous plastic waves with respect to a classical one-step strategy consisting in an a posteriori projection of the elastic trial stresses onto the yield locus. Elastic-plastic associated and non-associated constitutive models under small strains are considered in examples. In particular, dynamic ratchetting is simulated with the Armstrong-Frederick nonlinear kinematic hardening. Comparisons with respect to finite element numerical solutions show good agreements.

Mots clés: Elastic-plastic solids; Lax-Wendroff; Associated and non-associated plasticity

Domaines: Mécanique des solides [physics.class-ph]; Modélisation et simulation

Thomas Heuzé. Lax-Wendroff schemes for elastic-plastic solids. Journal of Computational Physics, 2019, 396, pp.89-105. ⟨10.1016/j.jcp.2019.06.050⟩. ⟨hal-02279637⟩