On some recent advances in computational methods in the mechanics of fracture

Summary This paper provides an overview of some of the recent (1984–1988) developments in analytical/computational methods in the mechanics of fracture: (i) solution methods for the traction boundary integral equations for arbitrary-shaped cracks embedded in infinite solids, the crack-faces being subjected to arbitrary tractions; (ii) analytical solutions for elliptical or circular cracks embedded in isotropic or transversely isotropic solids (the crack-plane being at an arbitrary angle to the axis of transverse isotropy), with crack-faces being subjected to arbitrary tractions; (iii) finite-element or boundary-element alternating methods for two-dimensional crack-problems, as well as for three-dimensional problems of surface flaws in finite-dimensional structures of linear elastic solids; (iv) domain-integral methods in elastic-plastic or inelastic crack mechanics; and (v) methods for generation of weight-functions in 2 and 3-D linear elastic crack problems.