Two general integrals of singular crack tip deformation fields (Q1111821)

The Eshelby tensor E has vanishing divergence in a homogeneous elastic material, whereas the invariance of the crack tip J integral suggests, in accord with known solutions, that the product rE will have a finite limit at the tip. Here r is the distance from the tip. These considerations are shown to lead to two general integrals of the equations governing singular crack tip deformation fields. Some of their consequences are discussed for analysis of crack tip fields in linear and nonlinear materials.