Gradient formulation in coupled damage-plasticity (Q2774057)

The authors formulate a thermodynamically consistent multiscale gradient enhanced approach to coupled plasticity and damage. Thermodynamically consistent constitutive equations are derived in order to investigate such issues as size effect on the strength of the composite, the strain and damage localization effects on the macroscopic response of the composite, and the statistic inhomogeneity of the evolution-related damage variables associated with representative volume elements. This approach is based on nonlocal gradient-dependent theory of plasticity and damage over multiple scales that incorporates mesoscale internal state variables and their higher-order gradients at both macro- and mesoscales. The interaction of length scales is a paramount factor in understanding and controlling the material defects such as dislocation, voids and cracks at the mesoscale, and to interpret them at the macroscale. The behavior of these defects is captured not only individually, but also together with the interaction between them and their ability to create spatio-temporal patterns under different loading conditions. The purpose of the proposed model is to simulate properly size-dependent behavior of materials together with localization problems. Consequently, the boundary value problem of the standard continuum model remains well-posed even in the softening regime. The description of gradient-enhanced continuum results in additional partial differential equations that are satisfied in weak form. Additional nodal degrees of freedom are introduced, which leads to a modified finite element formulation. The governing equations can be consistently linearized and solved within an incremental iterative Newton-Raphson procedure.