A numerical study of two‐dimensional spontaneous rupture propagation

Abstract

We present a numerical technique to determine the displacement and stress fields due to propagation of two‐dimensional shear cracks in an infinite, homogeneous medium which is linearly elastic everywhere off the crack plane. Starting from the representation theorem, an integral equation for the displacements inside the crack is found. This integral equation is solved by a method proposed by Hamano for various initial and boundary conditions on the crack surface. We verified the accuracy of our numerical method by comparing it with the analytical solution of Kostrov, and the numerical solution of Madariaga. A critical stress jump across the tip of a crack (between a grid‐point inside the crack and a neighbouring point out‐side the crack) is used as our fracture criterion. We find that our critical stress jump is the finite difference approximation to the critical stress‐intensity factor used in Irwin's fracture criterion. For an in‐plane shear crack starting from the Griffin critical length and controlled by the above fracture criterion, the propagation velocity of the crack‐tip is found to be sub‐Rayleigh or super‐shear depending on the strength of the material (given by the critical stress jump) and the instantaneous length of the crack. In fact, the crack‐tip velocity may even reach the P‐wave velocity for low‐strength materials. Additionally we find that once the crack starts propagating, it accelerates rapidly to its terminal velocity, and that the average rupture velocity over an entire length of fault cannot be much smaller than the terminal velocity, for smooth rupture propagation. Copyright © 1977, Wiley Blackwell. All rights reserved