Coupling Continuum Damage Mechanics and Discrete Fracture Models: A Geomechanics Perspective

Abstract

We present numerical methods to simulate the propagation of discrete fractures embedded in a damaged zone. Continuum Damage Mechanics (CDM) models are implemented in a Finite Element (FE) analysis code. A damage threshold defines the beginning of micro-crack coalescence, when a discrete cohesive segment opens. First, Cohesive Zone (CZ) elements are inserted between volume elements. The length and orientation of the discrete fracture are controlled by the magnitude of the energy released at integration points. The fracture path highly depends on space discretization, but the damage threshold is calculated automatically upon CDM model calibration. Second, an eXtended Finite Element Method (XFEM) approach is proposed. The fracture path is a function of the weighted average direction of maximum damage. Fracture growth depends on a nonlocal internal length, and the damage threshold is set empirically. Both coupling methods perform satisfactorily for simulating pure mode I or pure mode II fracture propagation resulting from micro-crack coalescence. However, the derivation of the Jacobian matrix in the XFEM makes it impractical to couple CDM and CZ models when the damaged stiffness cannot be expressed explicitly. For mixed mode fracture propagation and bifurcation problems, CZ insertion shows great promise, but mesh dependency and computational cost remain challenging.