A new discontinuous Galerkin method for non-linear Mechanics

A discontinuous Galerkin framework for large deformations of solids is established. The method is based on a general Hu-Washizu-de Veubeke functional allowing for displacement and stress discontinuities in the domain interior. The focus of this paper is on the treatment of large elasto-plastic deformations. The method is shown to possess the required numerical properties: consistency in the non-linear range and linearized stability. In order to demonstrate the versatility, accuracy and robustness of the method examples of application and convergence studies in three dimensions are provided. Further developments of the method will lead to applications where physical discontinuities must be modeled like fragmentation or failure