Finite strain primal interface formulation with consistently evolving stabilization

Abstract

SummaryA stabilized discontinuous Galerkin method is developed for general hyperelastic materials at finite strains. Starting from a mixed method incorporating Lagrange multipliers along the interface, the displacement formulation is systematically derived through a variational multiscale approach whereby the numerical fine scales are modeled via edge bubble functions. Analytical expressions that are free from user‐defined parameters arise for the weighted numerical flux and stability tensor. In particular, the specific form taken by these derived quantities naturally accounts for evolving geometric nonlinearity as well as discontinuous material properties. The method is applicable both to problems containing nonconforming meshes or different element types at specific interfaces and to problems consisting of fully discontinuous numerical approximations. Representative numerical tests involving large strains and rotations are performed to confirm the robustness of the method. Copyright © 2015 John Wiley & Sons, Ltd.