ON NONLOCAL DAMAGE MODELS FOR INTERFACE PROBLEMS

Consistent with thermodynamic restrictions, nonlocal formulations of d amage models are investigated with regard to their analytical and nume rical capabilities for predicting the evolution of microcracking. To t race the post-limit structural response with an efficient numerical al gorithm, an incremental-iterative solution strategy is constructed thr ough the use of an initial elasticity stiffness matrix and an evolving -localization constraint. The constraint is related to a suitable meas ure of microcracking at the most severely damaged element that changes with the evolution of a localization zone. As a simple phenomenologic al approach, a nonlocal feature is incorporated into the constitutive model through the gradient of a scalar measure of damage, and a symmet ry boundary condition is invoked for the nonlocal governing differenti al equation. In numerical calculations, the gradient is evaluated thro ugh a simple difference scheme. For applications to the interface prob lems with geologic media, the proposed procedure is verified with anal ytical solutions for one-dimensional cases, and illustrated with two-d imensional cases for which experimental observations are available. So me important theoretical and computational issues associated with nonl ocal models are then discussed based on the results obtained.