Abstract
We compare two methods for calculating the energy released during quasi-static crack advance. One method is based on a surface integral (line integral in two dimensions) expression for the energy release rate, whereas the other method is based on a volume (area) integral representation. A concise derivation of the volume (area) integral expression is given using a virtual-work-type identity for Eshelby's energy momentum tensor. The finite-element implementation of the volume (area) integral formulation corresponds to the virtual crack extension method. Within the context of this formulation, we outline a procedure for calculating pointwise values of the energy release rate along a three-dimensional crack front. For illustrative purposes, numerical examples are presented for a fully plastic, plane strain, edge-cracked panel subject to combined tension and bending.
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