2D Fracture Network Mathematics

2D elastostatic displacement solutions for the Yoffe Mode I and Rice Mode II crack models are reviewed. These solutions are used to introduce the elastostatic displacement solution for a 2D Mode I/II multi-crack configuration in terms of meromorphic differential forms on a hyperelliptic curve. Using the multi-crack solution, a picture of crack growth as motion of a point in a moduli space of Riemann surfaces is presented, whereby the the final rupture configuration of the crack may be associated with a singular Riemann surface such as a Riemann sphere with a pair of points identified.