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Some numerical studies of crack propagation are based on using constitutivemodels that account for damage evolution in the material. When a critical damage value hasbeen reached in a material point, it is natural to assume that this point has no more carryingcapacity, as is done numerically in the element vanish technique. In the present review this procedureis illustrated for micromechanically based material models, such as a ductile failuremodel that accounts for the nucleation and growth of voids to coalescence, and a model for intergranularcreep failure with diffusive growth of grain boundary cavities leading to micro–crack formation. The procedure is also illustrated for low cycle fatigue, based on continuumdamage mechanics. In addition, the possibility of crack growth predictions for elastic–plasticsolids using cohesive zone models to represent the fracture process is discussed.