An investigation of numerical method for three-dimensional elastic-plastic flows

A cell-centered Lagrangian discontinuous Galerkin (DG) method is developed for simulating elastic-plastic flows on three-dimensional unstructured hexahedral meshes. The elastic-plastic deformation is described by the hypo-elastic model with Jaumann stress rate, while plasticity is computed using the radial return algorithm. The elastic limit state is governed by the von Mises yield condition, with yield strength determined by either perfectly plastic model, linear hardening model, or Johnson-Cook model. A new Riemann solver for three-dimensional elastic-plastic problems is constructed, in which the Cauchy stress tensor is calculated at the centers of the triangular facets of the hexahedral elements and then used to compute the numerical fluxes of the semi-discrete equations for the conserved variables. Furthermore, a novel nodal solver is developed for calculating velocities of both interior nodes and boundary nodes subject to various boundary conditions. This nodal solver operates on all sub-triangular facets surrounding each node, rigorously enforcing global conservation of both total energy and momentum while satisfying entropy inequality constraints. The DG coefficients of the conserved variables and the deviatoric stress tensor are updated by using a second-order total variation diminishing Runge-Kutta time integration scheme. A least squares reconstruction algorithm with Barth-Jesperson limiter is used to eliminate the non-physical numerical oscillation of the conserved variables and the deviatoric stress tensor. Due to the high computational cost of three-dimensional simulations, a parallel algorithm on unstructured hexahedral meshes is implemented to improve efficiency. Several numerical tests and a projectile impact experiment are conducted to validate the proposed scheme. Experimental validations and numerical results confirm the accuracy and robustness of the scheme developed in this work.