With some knowledge of the suspected failure mechanisms, numerical models may be created to capture failure behavior within a particular material. These specialized numerical failure models can be used to predict the behavior of the specific material after the onset of failure mechanisms. Within this work specialized failure models are developed to analyze the behavior of failing materials within three material systems: a brittle matrix filled with stiff platelets, an elastomer matrix filled with graphene nanoplatelets, and an elastoplastic geomaterial.;Failure within the first system, a solid consisting of a brittle matrix filled with discontinuous platelets, may occur when a matrix crack grows unimpeded. Platelets bridging a crack may toughen the composite. However, this toughening is highly dependent on the interface between the matrix and the platelets. A numerical interface model is constructed and a crack is bridged with platelets with both a very strong interface and a stick-slip interface. It is found that if the interface is too strong it creates secondary stress concentrations that could damage previously uncracked matrix while a tailored stick-slip interface can still bridge the crack and limit secondary stress concentrations.;Failure in the second system, an elastomer matrix filled with graphene nanoplatelets, occurs by tearing in the elastomer. Recent experimental evidence has shown that with enough filler, both the failure strain and failure stress of the elastomer improve with increasing filler concentration. Beyond an optimum concentration the failure strain decreases. A numerical lattice model is built that captures the behavior of the composite. The model is able to identify the distributed deformation mechanisms responsible for these improvements in failure stress and strain as well as the reason for the reversal in failure strain.;The third material, elastoplastic geomaterials, fails by strain localization. A numerical finite element model is developed that can detect the strain localization instabilities, add these localizations in the finite element model with the extended finite element method, and model these failures as newly added contact surfaces. This allows material to be modeled beyond the initial localization failure. The usefulness of this model is demonstrated on a soil slope under eccentric loading.
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