Quasi-static hydraulic crack growth driven by Darcy's law
| dc.contributor.area | Mathematics | en_US |
| dc.contributor.author | Almi, Stefano | |
| dc.date.accessioned | 2016-06-23T09:18:19Z | |
| dc.date.available | 2016-06-23T09:18:19Z | |
| dc.date.issued | 2016 | |
| dc.description.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. | en_US |
| dc.identifier.uri | https://openscience.sissa.it/handle/1963/35198 | |
| dc.language.iso | en | en_US |
| dc.miur.area | 1 | en_US |
| dc.relation.ispartofseries | SISSA;29/2016/MATE | |
| dc.subject | variational models, free-discontinuity problems, crack propagation, brittle fractures, hydraulic fractures, quasi-static evolution, energy release rate, Griffith’s criterion | en_US |
| dc.subject.miur | MAT/05 | en_US |
| dc.title | Quasi-static hydraulic crack growth driven by Darcy's law | en_US |
| dc.type | Preprint | en_US |