TY - RPRT
T1 - Quasi-static hydraulic crack growth driven by Darcy's law
Y1 - 2016
A1 - Stefano Almi
AB - 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.
UR - http://urania.sissa.it/xmlui/handle/1963/35198
U1 - 35492
U2 - Mathematics
U4 - 1
U5 - MAT/05
ER -