A Precis of Two-Scale Approaches for Fracture in Porous Media

R. Borst, de, J. Rethore, M.A. Abellan

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

5 Citations (Scopus)

Abstract

A derivation is given of two-scale models that are able to describe deformation and flow in a fluid-saturated and progressively fracturing porous medium. From the micromechanics of the flow in the cavity, identities are derived that couple the local momentum and the mass balances to the governing equations for a fluid-saturated porous medium, which are assumed to hold on the macroscopic scale. By exploiting the partition-of-unity property of the finite element shape functions, the position and direction of the fracture is independent from the underlying discretisation. The finite element equations are derived for this two-scale approach and integrated over time. The resulting discrete equations are nonlinear due to the cohesive crack model and the nonlinearity of the coupling terms. A consistent linearisation is given for use within a Newton—Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach.
Original languageEnglish
Title of host publicationLecture Notes on Composite Materials
Place of PublicationBerlin
PublisherSpringer
Pages149-171
ISBN (Print)978-1-4020-8771-4
DOIs
Publication statusPublished - 2009

Publication series

NameSolid Mechanics and its applications
Volume154
ISSN (Print)0925-0042

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porous medium
micromechanics
fluid
nonlinearity
mass balance
momentum
cavity
crack

Cite this

Borst, de, R., Rethore, J., & Abellan, M. A. (2009). A Precis of Two-Scale Approaches for Fracture in Porous Media. In Lecture Notes on Composite Materials (pp. 149-171). (Solid Mechanics and its applications; Vol. 154). Berlin: Springer. https://doi.org/10.1007/978-1-4020-8772-1_5
Borst, de, R. ; Rethore, J. ; Abellan, M.A. / A Precis of Two-Scale Approaches for Fracture in Porous Media. Lecture Notes on Composite Materials. Berlin : Springer, 2009. pp. 149-171 (Solid Mechanics and its applications).
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Borst, de, R, Rethore, J & Abellan, MA 2009, A Precis of Two-Scale Approaches for Fracture in Porous Media. in Lecture Notes on Composite Materials. Solid Mechanics and its applications, vol. 154, Springer, Berlin, pp. 149-171. https://doi.org/10.1007/978-1-4020-8772-1_5

A Precis of Two-Scale Approaches for Fracture in Porous Media. / Borst, de, R.; Rethore, J.; Abellan, M.A.

Lecture Notes on Composite Materials. Berlin : Springer, 2009. p. 149-171 (Solid Mechanics and its applications; Vol. 154).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

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AB - A derivation is given of two-scale models that are able to describe deformation and flow in a fluid-saturated and progressively fracturing porous medium. From the micromechanics of the flow in the cavity, identities are derived that couple the local momentum and the mass balances to the governing equations for a fluid-saturated porous medium, which are assumed to hold on the macroscopic scale. By exploiting the partition-of-unity property of the finite element shape functions, the position and direction of the fracture is independent from the underlying discretisation. The finite element equations are derived for this two-scale approach and integrated over time. The resulting discrete equations are nonlinear due to the cohesive crack model and the nonlinearity of the coupling terms. A consistent linearisation is given for use within a Newton—Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach.

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T3 - Solid Mechanics and its applications

SP - 149

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BT - Lecture Notes on Composite Materials

PB - Springer

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Borst, de R, Rethore J, Abellan MA. A Precis of Two-Scale Approaches for Fracture in Porous Media. In Lecture Notes on Composite Materials. Berlin: Springer. 2009. p. 149-171. (Solid Mechanics and its applications). https://doi.org/10.1007/978-1-4020-8772-1_5