@article {10829,
	title = {A variational model for the quasi-static growth of fractional dimensional brittle fractures},
	number = {Interfaces and Free Boundaries},
	year = {2014},
	publisher = {European Mathematical Society},
	abstract = {<p>We propose a variational model for the irreversible quasi-static evolution of brittle fractures having fractional Hausdorff dimension in the setting of two-dimensional antiplane and plane elasticity. The evolution along such irregular crack paths can be obtained as $\Gamma$-limit of evolutions along one-dimensional cracks when the fracture toughness tends to zero.</p>},
	keywords = {Variational models},
	doi = {10.4171/IFB/328},
	url = {http://hdl.handle.net/1963/6983},
	author = {Simone Racca and Rodica Toader}
}
@article {2012,
	title = {A Viscosity-driven crack evolution},
	journal = {Advances in Calculus of Variations 5 (2012) 433-483},
	number = {SISSA;63/2011/M},
	year = {2012},
	publisher = {SISSA},
	abstract = {<p>We present a model of crack growth in brittle materials which couples dissipative effects on the crack tip and viscous effects. We consider the 2 -dimensional antiplane case with pre-assigned crack path, and firstly prove an existence result for a rate-dependent evolution problem by means of time-discretization. The next goal is to describe the rate-independent evolution as limit of the rate-dependent ones when the dissipative and viscous effects vanish. The rate-independent evolution satisfies a Griffith{\textquoteright}s criterion for the crack growth, but, in general, it does not fulfil a global minimality condition; its fracture set may exhibit jump discontinuities with respect to time. Under suitable regularity assumptions, the quasi-static crack growth is described by solving a finite-dimensional problem.</p>},
	doi = {10.1515/acv-2011-0012},
	url = {http://hdl.handle.net/1963/5130},
	author = {Simone Racca}
}
