Propagation of a shock discontinuity in an elasto-plastic material: constitutive relations
Résumé
The shock discontinuity problem is analyzed in the case of elastoplastic materials ; the jump relations for internal state variables cannot be exhibited directly. For this purpose, we solve the internal shock structure problem, assuming that the shock front is a continuous transition in a thin layer, taking account of dissipative effects. The shock generating function is introduced. The canonical equations of the shock structure are determined in the general case when the evolution of plasticity is derived from a pseudo potential of dissipation. The plane wave is analyzed for an isotropic material obeying a von Mises criterion, assuming that inside the shock the material is under pure axial compression: the existence and uniqueness results are established.