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Propagation of a shock discontinuity in an elasto-plastic material: constitutive relations

Dequiedt J. L., Stolz C.

Archives of Mechanics

2004

Vol. 56, nr 5

391-410

The shock discontinuity problem is analyzed in the case of elasto-plastic 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 P 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 D. 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.