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 -
TY - THES
T1 - Some results on the mathematical analysis of crack problems with forces applied on the fracture lips
Y1 - 2016
A1 - Stefano Almi
KW - Fracture mechanics
AB - This thesis is devoted to the study of some models of fracture growth in elastic materials, characterized by the presence of forces acting on the crack lips. Working in the general framework of rate-independent processes, we first discuss a variational formulation of the problem of quasi-static crack evolution in hydraulic fracture. Then, we investigate the crack growth process in a cohesive fracture model, showing the existence of an evolution satisfying a weak Griffith's criterion. Finally, in the last chapter of this work we investigate, in the static case, the interaction between the energy spent in order to create a new fracture and the energy spent by the applied surface forces. This leads us to study the lower semicontinuity properties of a free discontinuity functional F(u) that can be written as the sum of a crack term, depending on the jump set of u, and of a boundary term, depending on the trace of u.
PB - SISSA
U1 - 35503
U2 - Mathematics
U4 - 1
U5 - MAT/05
ER -
TY - RPRT
T1 - A lower semicontinuity result for a free discontinuity functional with a boundary term
Y1 - 2015
A1 - Stefano Almi
A1 - Gianni Dal Maso
A1 - Rodica Toader
AB - We study the lower semicontinuity in $GSBV^{p}(\Om;\R^{m})$ of a free discontinuity functional~$\F(u)$ that can be written as the sum of a crack term, depending only on the jump set~$S_{u}$, and of a boundary term, depending on the trace of~$u$ on~$\partial\Om$. We give sufficient conditions on the integrands for the lower semicontinuity of~$\F$. Moreover, we prove a relaxation result, which shows that, if these conditions are not satisfied, the lower semicontinuous envelope of~$\F$ can be represented by the sum of two integrals on~$S_{u}$ and~$\partial\Om$, respectively.
UR - http://urania.sissa.it/xmlui/handle/1963/35146
U1 - 34731
U2 - Mathematics
U4 - 1
U5 - MAT/05
ER -
TY - JOUR
T1 - Quasi-static crack growth in hydraulic fracture
Y1 - 2014
A1 - Stefano Almi
A1 - Gianni Dal Maso
A1 - Rodica Toader
AB - 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.
PB - Elsevier
UR - http://urania.sissa.it/xmlui/handle/1963/34532
U1 - 34741
U2 - Mathematics
U4 - 1
U5 - MAT/05
ER -