Gradient formulation in coupled damage-plasticity

This work provides a consistent and systematic framework for the gradient approach in coupled damage-plasticity that enables one to better understand the effects of material inhomogeneity on the macroscopic behavior and the material instabilities. The idea of multiple scale effects is made more general and complete by introducing damage and plasticity internal state variables and the corresponding gradients at both the macro and mesoscale levels. The mesoscale gradient approach allows one to obtain more precise characterization of the nonlinearity in the damage distribution; to address issues such as lack of statistical homogeneous state variables at the macroscale level such as debonding of fibers in composite materials, crack, voids, etc., and to address nonlocal influences associated with crack interaction. The macroscale gradients allow one to address non-local behavior of materials and interpret the collective behavior of defects such as dislocations and cracks. The development of evolution equations for plasticity and damage is treated in a similar mathematical approach and formulation since both address defects such as dislocations for the former and cracks/voids for the latter. Computational issues of the gradient approach are introduced in a form that can be applied using the finite element approach.