Strain energy release rate calculation from 3-D singularity finite elements

Two expressions for the strain energy release rate for threedimensional singularity finite elements are derived based on the Irwin's virtual crack closure method. The strain energy release rate for the three modes of fracture mechanics can be separately calculated from the nodal forces ahead of the crack front and the opening displacements behind it. The material is assumed to be isotropic. The stress distribution is written in terms of the eight nodal forces of the crack front element, and the crack opening displacement function is expressed in terms of the nodal opening displacement behind the crack front. The derived formula is a bit complicated because it involves eight nodal forces and five opening displacements. Therefore, a modification is made to get a simpler formula by eliminating some of the nodal forces from the original one. Comparisons with some problems from the literature indicate that the derived formulae are accurate for the computation of the strain energy release rate from 3-D singularity finite elements.