A novel variational framework for an interface zone model is developed and extended to poroelasticity. As was previously promoted in [1,2], the total energy of the system is composed by the bulk potential and fracture surface energy. In contrast to the phase‐field method, the fracture surface is approximated directly along the edges of the finite elements in terms of interface zero‐thickness finite elements. By introducing a new degree of freedom c (damage field) on the interface level, the solution is found by the minimization of the total potential energy with respect to the displacements and the damage field. An elastic interface constitutive law allowing for a normal and tangential displacement opening is adopted in the pre‐fracture regime. Assuming, that a crack propagates according to the Griffith's criterion of brittle fracture, fracture initiates and propagates in normal opening mode. Biot's theory is applied both to the bulk and interface elements for the simulation of fluid driven fracture in fully saturated materials. The pressure field within the interfaces is averaged between the pressure at the bulk element faces. Pressure continuity is enforced by means of a penalty functional. The flow within the fracture is modeled by the cubic law taking the displacement and damage variables into account. A number of numerical benchmark tests, which include comparisons with experimental results and analytical solutions, are performed to demonstrate the performance of the model. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Proceedings in Applied Mathematics & Mechanics – Wiley
Published: Jan 1, 2017
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