The ductile fracture of many materials is related to the nucleation, growth, and coalescence of voids. Also, a material containing voids represents an extreme case of heterogeneous materials. In the last few decades, numerous studies have been devoted to the local deformation mechanisms and macroscopic overall properties of nonlinear materials containing voids. This article presents a critical review of the studies in three interconnected topics in nonlinear mechanics of materials containing isolated voids, namely, the growth of an isolated void in an infinite medium under a remote stress; the macroscopic mechanical behavior of these materials predicted by using a cell model; and bounds and estimates of the overall properties of these materials as a special case of nonlinear composite materials. Emphasis are placed upon analytical and semianalytical approaches for static loading conditions. Both the classical methods and more recent approaches are examined, and some inadequacies in the existing methods are pointed out. In addition to the critical review of the existing methods and results, some new results, including a power-law stress potential for compressible nonlinear materials, are presented and integrated into the pertinent theoretical frameworks. This review article contains 118 references.

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