A framework for constitutive relations and failure criteria for materials with distributed properties, with application to porous viscoplasticity (Q1354930)

A framework is presented for constitutive equations and failure criteria for materials whose properties are not adequately representable as averages, but where the distribution of material properties must be taken into account. The framework describes the evolution of the distribution with deformation and allows failure criteria to be formulated based on a much more complete knowledge of the state of the material. This framework allows a number of processes, such as ductile fracture, dynamic recrystallization and composite failure, which are intrinsically dependent on the distribution of the material properties at a microscopic level, to be modeled in a way that was not possible previously. The framework can also be used as a tool to probe the actual interactions between parts of a body with distributed properties. An integration procedure is proposed which dramatically reduces the numerical effort involved in implementing this framework for certain problems.