### Abstract

Original language | English |
---|---|

Title of host publication | Lecture Notes on Composite Materials |

Place of Publication | Berlin |

Publisher | Springer |

Pages | 149-171 |

ISBN (Print) | 978-1-4020-8771-4 |

DOIs | |

Publication status | Published - 2009 |

### Publication series

Name | Solid Mechanics and its applications |
---|---|

Volume | 154 |

ISSN (Print) | 0925-0042 |

### Fingerprint

### Cite this

*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

}

*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

TY - CHAP

T1 - A Precis of Two-Scale Approaches for Fracture in Porous Media

AU - Borst, de, R.

AU - Rethore, J.

AU - Abellan, M.A.

PY - 2009

Y1 - 2009

N2 - 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.

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.

U2 - 10.1007/978-1-4020-8772-1_5

DO - 10.1007/978-1-4020-8772-1_5

M3 - Chapter

SN - 978-1-4020-8771-4

T3 - Solid Mechanics and its applications

SP - 149

EP - 171

BT - Lecture Notes on Composite Materials

PB - Springer

CY - Berlin

ER -