Cracks in anisotropic media: pseudodifferential equations, wave fronts, and Irwin’s energy release rate extension

Abstract

3D problems for plane cracks of arbitrary shape in anisotropic media are considered. The stress intensity factors are determined by the intensity factors of the crack displacement discontinuity field. Strong ellipticity of the constructed pseudodifferential operator is proved. The solution of the pseudodifferential operator of the crack theory is obtained by the specially constructed potentials with densities concentrated at the crack front. Irwin’s relation for the energy release rate is obtained for a plane crack of arbitrary shape in a medium with arbitrary elastic anisotropy.