An artificial viscosity, Lagrangian finite element method for capturing shocks in largely-deforming elastic-plastic materials

A method is presented for capturing shock discontinuities appearing in elastic and plastic solids. The approach is based on a Lagrangian finite element formulation for solids undergoing large, possibly plastic, deformations and a formulation of artificial viscosity. The proposed artificial viscosity method is formulated at the constitutive level and, therefore, independent of the dimension of space and of the particular finite element interpolation. Furthermore, it is material frame indifferent. The analysis of the method is restricted in this work to two and three–dimensional quadratic elements. The correctness of the method is verified by comparing the numerical and exact solution for the Riemann problem in perfect gases in two dimensions and by checking the jump conditions and shock propagation velocity in tantalum. The behavior of tantalum up to extreme loads of the order of 200GPa is modeled by recourse to an equation of state derived by Cohen et al from ab initio quantum mechanical calculations ([19]) and by a SteinbergGuinan J2-isotropic large-deformation plasticity model that accounts for rate dependency and thermal softening effects ([5]). The model is used to simulate a plate impact experiment with an impact speed V = 2000m/sec.