Mohammadreza Hirmand

Abstract:

Crack propagation is most frequently implemented on the basis of so-called extrinsic models in which discontinuity surfaces (cracks) are introduced upon satisfaction of an external stress criterion. Often, an implicit time marching scheme is employed in which the crack is kept fixed within the computations of the iterative solver. The crack is advanced to a pre-determined length on the basis of a pre-determined propagation law at the end of the load step. This approach has been shown to lack mathematical soundness and is especially problematic in the context of hydraulic fracturing. The sequential solution of the displacement and crack surface in unknown fields leads to crack propagation velocities that do not converge with time step and mesh size refinement. A consequence of this issue is that the hydraulic fracturing model cannot properly capture the step-wise crack advancement and pressure oscillations in saturated porous media. This is not a coincidence but a manifestation of robustness issues with extrinsic crack propagation algorithms. We propose a hydraulic fracturing model with non-differentiable energy minimization for cohesive fracture in which formation and propagation of cracks are direct outcomes of the computations within the time step. The method allows advancement for any length of crack within a time step given the applied loads without need to introduce crack nucleation and crack increment length criteria. Numerical results show step-wise behavior which also exhibit convergence with time step and mesh size refinement.

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