Abstract
This article devotes to an attempt at reviewing mathematical and computational studies in fracture mechanics. However, since the related literature is considerably vast, the selected topics are almost confines to the regime of elastic fracture mechanics. Furthermore, only fundamental aspects constituting the basis of the current fracture mechanics are reviewed. The relevant major topics are (i) asymptotic eigen expansions of various crack-tip fields, (ii) the VNA solution for an elliptical crack subject to arbitrary traction forces and its applications to the Schwartz-Neumann alternating method, (iii) path-independent integrals, (iv) three basic types in fracture simulation, and (v) hybrid numerical methods in fracture mechanics researches.
