One-Dimensional Failure Modes for Bodies with Non-convex Plastic Energies

Abstract In this paper, a complete picture of the different plastic failure modes that can be predicted by strain gradient plasticity model proposed in Del Piero et al. (J. Mech. Mater. Struct. 8:109–151, 2013) is drawn. The evolution problem elasto-plastic formulated as an incremental minimization acting on energy functional which includes local term and non-local contribution. Here, approximate analytical solution determined one-dimensional case tensile bar. Different solutions are found describing specific processes, correlations between convexity/concavity properties density established. variety demonstrates large versatility many mechanisms, ranging from brittle to ductile. Indeed, for convex energy, diffuses body, while, concave it localizes regions whose amplitude depends internal length parameter included into term, and, depending convexity first derivative localization band expands or contracts. Complex processes combining reproduced assuming functionals with branches. quasi-brittle geomaterials simple tension tests was convex-concave accuracy predictions checked comparing them numerical results finite element simulations.