The paper reviews recent work on fundamentals of elastic-plastic finite-element analysis and its applications to the mechanics of crack opening and growth in ductile solids. The presentation begins with a precise formu~tion of incremental equilibrium equations and their finite-element forms in a marines valid for deformations of arbitrary magnitude. Special features of computational procedures are outlined for accuracy in view of the near-incompressibility of elastic-plastic response. Applications to crack mechanics include the analysis of large plastic deformations at a progressively opening crack tip, the determination of J integral values and of limitations to I characterizations of the intensity of the crack tip field, and the determination of crack tip fields in stable crack growth
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