Abstract
This paper presents an unconventional method for examining various kinematically admissible and physically acceptable mechanisms of dilatant deformation in ductile materials. In this approach, the constitutive description of material behavior is intentionally left incomplete, i.e., shear stresses and strain rates obey power law, but while material dilatancy is allowed to exist, its form is not predetermined. By omitting the constitutive equation for dilatancy, multiple boundary value solutions can be obtained; these solutions can be further examined and evaluated using an energy minimization criterion. The proposed method allows plausible constitutive assumptions for cavitation to be identified. Using this method, we show that in the vicinity of a mode I crack tip, there are three distinct mechanisms of dilatant deformation, each having strong experimental justification.
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