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The Exclusion Region theory is a new theoretical construct that attempts to address both the difficulty of solving the boundary-value problem in the presence of a crack, and the subsequent difficulty of extracting from the solution a physically relevant fracture criterion. The theory starts with the presumption that, within a small radius of the separation front, the stress field as determined from the local constitutive model does not provide a meaningful representation of the internal force distribution for purposes of imposing equilibrium. Equilibrium (or momentum conservation) therefore cannot be applied pointwise within this exclusion region to solve for the displacement field. Instead, the material displacement field within the exclusion region is given by an assumed form that accommodates the separation of a material surface into a pair of new free surfaces. The enriched kinematics of the exclusion region may therefore be regarded as simply leading to a broadened constitutive model, which only applies to a small material neighborhood that is suffering surface separation. Further, and in contrast to conventional fracture mechanics, the form of the crack advance criterion does not restrict the material model that may be applied in the bulk continuum. The Exclusion Region theory has been implemented in a two-dimensional finite element code. The code uses a novel numerical procedure in which the moving separation front lies at the center of a translating, disc-shaped patch of elements. Compatibility at the interface between the mesh patch and the fixed background mesh is enforced weakly. Numerical studies have demonstrated complete correspondence between the new theory and linear elastic fracture mechanics. Preliminary results involving large deformations and extensive plastic deformation are also presented.
elastic-plastic fracture, computational methods, crack extension
Associate Professor, University of California at Davis, Davis, CA
Graduate Research Assistant,