Variational interface zone model for modeling of fluid induced fracture propagation

Variational interface zone model for modeling of fluid induced fracture propagation 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) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings in Applied Mathematics & Mechanics Wiley

Variational interface zone model for modeling of fluid induced fracture propagation

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2017 Wiley Subscription Services
ISSN
1617-7061
eISSN
1617-7061
D.O.I.
10.1002/pamm.201710029
Publisher site
See Article on Publisher Site

Abstract

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)

Journal

Proceedings in Applied Mathematics & MechanicsWiley

Published: Jan 1, 2017

References

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