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/1963/3519800712nas a2200157   4500008004100000245005200041210005100093260001300144300001200157490000800169520027400177100001800451700002100469700001900490856004500509       2014                        en  d00aQuasi-static crack growth in hydraulic fracture0 aQuasistatic crack growth in hydraulic fracture  bElsevier  a301-3180 v1093 a<p>We present a variational model for the quasi-static crack growth in hydraulic fracture in the framework of the energy formulation of rate-independent processes. The cracks are assumed to lie on a prescribed plane and to satisfy a very weak regularity assumption.</p>1 aAlmi, Stefano1 aDal Maso, Gianni1 aToader, Rodica  uhttp://hdl.handle.net/20.500.11767/17350