8 - Quasistatic crack growth in heterogeneous media

Abstract

This chapter is devoted to the problem of quasistatic crack growth in heterogeneous elastic media. The method of fast solution of the crack problem developed in Chapter 6 opens the way for efficient numerical simulation of crack growth by increasing external loading. First, the method is applied to simulation of crack growth under prescribed pressure applied to the crack surface (Sections 8.1 and 8.2). Then, crack growth caused by fluid injected inside the crack is considered. This problem relates to the so-called hydraulic fracture that is widely used in oil and gas exploration technology. The coupled problem of solid, fluid, and fracture mechanics for simulation of hydraulic fracture is considered. For numerical solution of the governing equations of the hydraulic fracture theory, the discrete model of crack propagation is proposed (Section 8.3). An approximate three-parameter model considered in Section 8.4 accelerates substantially computer simulations of hydraulic fracture processes. Numerical examples and computational programs for simulation of crack propagation in heterogeneous media are presented.