A Variational Model for Plastic Slip and Its Regularization via Γ -Convergence

摘要: A variational model is presented able to interpret the onset of plastic deformations, here modeled as displacement jumps occurring along slip surfaces at constant yielding stress. The corresponding strain energy functional, leading a free-discontinuity problem set in space SBV functions, then approximated by sequence regularized elliptic functionals following seminal work Ambrosio and Tortorelli (Commun. Pure Appl. Math. 43, 999–1036, 1990) within framework Γ-convergence. Comparisons between results obtainable with its approximation, terms stability pure elastic phase, irreversibility response under unloading, are presented, general, for 2-D case antiplane shear exemplified, particular, 1-D case.