Calculus of Variations and Geometric Measure Theory
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S. Almi

Quasi-static hydraulic crack growth driven by Darcy's law

created by almi on 18 Jun 2016

[BibTeX]

Preprint

Inserted: 18 jun 2016
Last Updated: 18 jun 2016

Year: 2016

Abstract:

In the framework of rate independent processes, we present a variational model of quasi-static crack growth in hydraulic fracture. We first introduce the energy functional and study the equilibrium conditions of an unbounded linearly elastic body subject to a remote strain ε ∈ R and with a sufficiently regular crack Γ filled by a volume V of incompressible fluid. In particular, we are able to find the pressure p of the fluid inside the crack as a function of Γ, V , and ε. Then, we study the problem of quasi-static evolution for our model, imposing that the fluid volume V and the fluid pressure p are related by Darcy’s law. We show the existence of such an evolution, and we prove that it satisfies a weak notion of the so-called Griffith’s criterion.


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