Longitudinal shock waves in solids: the piston shock analogue

Abstract

Propagation of longitudinal deformation in hardening elastoplastic solids is investigated by the way of analogy with the shock tube pattern in fluid mechanics. Conditions for the appearance of a shock discontinuity are formulated and steady-state continuous and discontinuous solutions are derived. Field characteristics are then investigated for a representative family of hardening elastoplastic Mises solids accounting for finite strains. A critical limit value of the imposed velocity for the emergence of a shock wave is found and sensitivity to material parameters is assessed. Evaluation of dissipation effects is conducted and field response is compared with other uniaxial stress fields. In agreement with available experimental results, it is established that the field may consist of both an elastic precursor and a plastic shock separated by a continuous elastoplastic range. Or, alternatively, when the imposed velocity is higher, the plastic shock overtakes those regions allowing for a variety of resulting fields.