ARBITRARY DISCONTINUITIES IN THE NUMERICAL MANIFOLD METHOD

An overview of modeling arbitrary discontinuities within the numerical manifold method (NMM) framework is presented. The NMM employs a dual cover system, namely mathematical covers (MCs) and physical covers (PCs), to describe a physical problem. MCs are constructed totally independent of geometries of the problem domain, over which a partition of unity is defined. PCs are the intersections of MCs and the problem domain, over which local approximations with unknowns to be determined are defined. With such a dual cover system, arbitrary discontinuities involving jumps, kinks, singularities, and other nonsmooth features can be modeled in a convenient manner by constructing special PCs and designing tailored local approximations. Several typical discontinuities in solid mechanics are discussed. Among them are the simulations of material boundaries, voids, brittle cracks, cohesive cracks, material interfaces, interface cracks, dislocations, shear bands, high gradient zones, etc.