The concept of control points in hybrid discontinuous Galerkin methods—Application to geometrically nonlinear crystal plasticity

A new concept for hybrid discontinuous Galerkin (DG) methods is presented: control points. These are defined on the interelement boundaries. The concept makes it possible to formulate element shape functions without nodes. Moreover, the theory is not restricted to certain element shapes. Furthermore, one can formulate the discrete model such that the displacement is either continuous or discontinuous at the control points. Classical continuous isoparametric elements are included as special case. As an additional new feature, a regularization technique for very high strain rate sensitivity exponents up to 1000 in finite single crystal viscoplasticity is presented and implemented into the new hybrid DG framework. In addition, the numerical linearization used in an earlier work is carried out analytically in this work. To the knowledge of the authors, this work presents the first hybrid DG implementation of geometrically nonlinear plasticity, here in the context of single crystal plasticity. The regularization method in combination with the DG formulations facilitates a very simple implementation leading to a numerically efficient, robust, and locking‐free model. Two examples are investigated: the deformation of a planar double slip single crystal exhibiting localization in the form of shear bands and an oligocrystal under uniaxial load.