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Center for Nonlinear Studies |
The phenomenology of high-speed impact and penetration are of interest in many applica- tions including munition-target interatcions, geological impact dynamics, shock processing of powders, formation of shaped charges etc. In such high pressure physics problems, the hydro- dynamic pressure realized are often much greater than the strength of the material and hence the material undergoes elastic deformation followed by the plastic flow. In addition, the stress and strain fields are related through nonlinear elasto-plastic yield surfaces, the models for which must be included in the governing equations. In this work, a Lagrangian cell centered scheme based on mimetic operators, for capturing elasto-plastic response of solids is proposed. Since solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to the mass, momentum and energy conservation laws (mass is inherently conserved as mass exchange be- tween computational cells are prohibited). The governing equations in the discrete space are represented by mimetic operators, namely the discrete gradient, divergence and curl operators. Mimetic operators are constructed by mimicking fundamental vector and integral indentities and conservation laws as accurately as possible in the discrete space. The scheme is generic that it can be applied to arbitrary unstructured polygonal grids. The solver is godunov based. Geometric Conservation Law (GCL) and conservation of total energy are satisfied in the strong sense. In this model, the primitive variables are stored and evolved at the cell centers. Nodal velocities and half edge stress tensors are are defined and computed via a Riemann problem constructed at the nodes. The gas dynamics solver developed in [1] is extended to obtain the nodal velocity components and the half edge forces. The dilatational response of the material is modeled using the Mie-Gruneisen equation of state. The deviotaric stress components are evololved in accordance with hypo-elastic stress-strain relations. Plastic flow rule for strain hardening materials is enforced via a radial return algorithm based on J-2 Von Mises yield condition. The validity of the scheme is established via several benchmarking test cases with material models.
Host: Kim Rasmussen, T-5