ON NONLOCAL DAMAGE MODELS FOR INTERFACE PROBLEMS

Consistent with thermodynamic restrictions, nonlocal formulations of damage models are investigated with regard to their analytical and numerical capabilities for predicting the evolution of microcracking. To trace the post-limit structural response with an efficient numerical algorithm, an incremental-iterative solution strategy is constructed through the use of an initial elasticity stiffness matrix and an evolving-localization constraint. The constraint is related to a suitable measure of microcracking at the most severely damaged element that changes with the evolution of a localization zone. As a simple phenomenological approach, a nonlocal feature is incorporated into the constitutive model through the gradient of a scalar measure of damage, and a symmetry boundary condition is invoked for the nonlocal governing differential equation. In numerical calculations, the gradient is evaluated through a simple difference scheme. For applications to the interface problems with geologic media, the proposed procedure is verified with analytical solutions for one-dimensional cases, and illustrated with two-dimensional cases for which experimental observations are available. Some important theoretical and computational issues associated with nonlocal models are then discussed based on the results obtained.