Theoretical and computational methods for representing mechanical behaviors of crystalline materials in the vicinity of planar interfaces are examined and compared. Emphasis is on continuum-type resolutions of microstructures at the nanometer and micrometer levels, i.e., mesoscale models. Grain boundary interfaces are considered first, with classes of modelsencompassing sharp interface, continuum defect (i.e., dislocation and disclination), and diffuse interface types. Twin boundaries are reviewed next, considering sharp interface and diffuse interface (e.g., phase field) models as well as pseudoslip crystal plasticity approaches to deformation twinning. Several classes of models for evolving failure interfaces, i.e.,fracture surfaces, in single crystals and polycrystals are then critically summarized, including cohesive zone approaches,continuum damage theories, and diffuse interface models. Important characteristics of compared classes of models for a given physical behavior include complexity, generality/flexibility, and predictive capability versus number of free or calibrated parameters.
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