Computational Fracture Mechanics

This chapter examines areas of fracture mechanics that are being developed through computational stress analysis methods. Research of fracture mechanics is focused in two principal directions: (1) the development of phenomenological explanations of crack extension behaviors and (2) the description of micromechanical processes of material separation on a microscale. When the crack extension behavior of interest is accompanied by a small crack-tip plastic zone, the correlation is in terms of the elastic stress-intensity factor. Several numerical methods have been developed for this, including boundary collocation, numerical solution of integral equations, and finite elements. The boundary collocation method automatically satisfies traction-free boundary conditions on the crack surfaces. Another general method that has been used to obtain solutions for cracks is that of approximate conformal mapping, that may be applied to cracks emanating from holes in infinite bodies or to cracks at the edges in simply connected bodies. The technique involves finding accurate polynomial approximations to the mapping function that transforms the physical cracked domain into a circular region.