Simulation of hydraulic fracture of porous materials using the phase‐field modeling approach

In this contribution, the numerical simulation of hydraulic fracture of fluid‐saturated porous materials is carried out on a continuum‐mechanical scale using the theory of porous media (TPM), extended by a phase‐field modeling (PFM) approach. Following this, behaviors such as crack nucleation and propagation, solid matrix deformation and interstitial‐fluid flow change from Darcy to Stokes‐like flow in the cracked region can be realized. Moreover, permanent changes of the local physics due to occurrence of the crack, such as of the volume fractions and the permeability, are taken into consideration. The mathematical modeling of this problem yields a strongly coupled system of differential algebraic equations (DAE). Thus, special descretization schemes for a stable and efficient solution are needed. To reveal the ability of the proposed model to simulate the important features of hydraulic cracking, a two‐dimensional example using the finite element method is presented. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)