Calculation of path-dependent shock-wave hardening

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Abstract
Material hardening models can be divided broadly into two categories; those that depend on the path followed in getting to the final state and those that do not. For those that do not depend on the path, no special attention need be directed toward the case of shock fronts in numerical calculation. For those that do, however, care must be exercised in making sure that zone-size effects and artificial viscosity do not mask the real material behavior controlling the shear strength behind the shock wave. The mechanical threshold stress (MTS) model is an example of a path-dependent material constitutive description that requires such consideration. In this paper a procedure is established for treating shock waves in computations using the MTS model. It involves a means by which the presence of the shock wave and its peak amplitude is sensed and then performing a separate calculation to determine the material state immediately behind the shock.