A 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 param-eters 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 approxi-mations. Representative numerical tests involving large strains and rotations are performed to confirm the robustness of the method.
|Original language||English (US)|
|Number of pages||38|
|Journal||International Journal for Numerical Methods in Engineering|
|State||Published - Apr 2015|
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Applied Mathematics