@article {2016,
	title = {Quasi-static hydraulic crack growth driven by Darcy{\textquoteright}s law},
	number = {SISSA;29/2016/MATE},
	year = {2016},
	abstract = {<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{\textquoteright}s law. We show the existence of such an evolution, and we prove that it satisfies a weak notion of the so-called Griffith{\textquoteright}s criterion.</p>},
	url = {http://urania.sissa.it/xmlui/handle/1963/35198},
	author = {Stefano Almi}
}
