Abstract
Stress and strain discontinuities propagating in an elastic-plastic solid are examined within the small-deformation three-dimensional framework. Since in elastoplasticity, field quantities, in general, are history dependent, their possible jumps across a discontinuity surface depend on their variation within the thin transition zone which is often modeled as a discontinuity surface. The discontinuity relations associated with dynamic elasto-plastic problems are formulated in such a manner that all discontinuous field data are described in terms of only two stress components. Various special cases, such as incompressible solids, adiabatic deformations, plane strain problems, and quasistatic advance of discontinuities, are examined; for the quasistatic case, in particular, it is shown that all stress components are continuous and that, if the solid has positive work-hardening, then all strain components are also continuous.
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