01110nas a2200097   4500008004100000245006200041210006000103520078000163100001800943856005100961       2016                        en  d00aQuasi-static hydraulic crack growth driven by Darcy's law0 aQuasistatic hydraulic crack growth driven by Darcys law3 a<p>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.</p>1 aAlmi, Stefano  uhttp://urania.sissa.it/xmlui/handle/1963/35198