TY - RPRT
T1 - Energy-dissipation balance of a smooth moving crack
Y1 - 2018
A1 - Maicol Caponi
A1 - Ilaria Lucardesi
A1 - Emanuele Tasso
AB - In this paper we provide necessary and sufficient conditions in order to guarantee the energy-dissipation balance of a Mode III crack, growing on a prescribed smooth path. Moreover, we characterize the singularity of the displacement near the crack tip, generalizing the result in [S. Nicaise, A.M. Sandig - J. Math. Anal. Appl., 2007] valid for straight fractures.
UR - http://preprints.sissa.it/handle/1963/35320
U1 - 35630
U2 - Mathematics
U4 - 1
ER -
TY - RPRT
T1 - Existence of solutions to a phase field model of dynamic fracture with a crack dependent dissipation
Y1 - 2018
A1 - Maicol Caponi
AB - We propose a phase-field model of dynamic crack propagation based on the Ambrosio-Tortorelli approximation, which takes in account dissipative effects due to the speed of the crack tips. In particular, adapting the time discretization scheme contained in [Bourdin et al., Int. J. Fracture 168 (2011), 133-143] and [Larsen et al., Math. Models Methods Appl. Sci. 20 (2010), 1021-1048], we show the existence of a dynamic crack evolution satisfying an energy dissipation balance, according to Griffith's criterion.
UR - http://preprints.sissa.it/handle/1963/35307
U1 - 35614
U2 - Mathematics
U4 - 1
ER -
TY - RPRT
T1 - Linear hyperbolic systems in domains with growing cracks
Y1 - 2017
A1 - Maicol Caponi
AB - We consider the hyperbolic system $\ddot u-{\rm div}\,(\mathbb A\nabla u)=f$ in the time varying cracked domain $\Omega\setminus\Gamma_t$, where the set $\Omega\subset\mathbb R^d$ is open, bounded, and with Lipschitz boundary, the cracks $\Gamma_t$, $t\in[0,T]$, are closed subsets of $\overline\Omega$, increasing with respect to inclusion, and $u(t):\Omega\setminus\Gamma_t\to\mathbb R^d$ for every $t\in[0,T]$. We assume the existence of suitable regular changes of variables, which reduce our problem to the transformed system $\ddot v-{\rm div}\,(\mathbb B\nabla v)+\mathbf a\nabla v -2\nabla\dot vb=g$ on the fixed domain $\Omega\setminus\Gamma_0$. Under these assumptions, we obtain existence and uniqueness of weak solutions for these two problems. Moreover, we show an energy equality for the functions $v$, which allows us to prove a continuous dependence result for both systems.
UR - http://urania.sissa.it/xmlui/handle/1963/35271
U1 - 35577
U2 - Mathematics
U4 - 1
ER -