@article {1078-0947_2012_4_1125,
	title = {Second order approximations of quasistatic evolution problems in finite dimension},
	journal = {Discrete \& Continuous Dynamical Systems - A},
	volume = {32},
	number = {1078-0947_2012_4_112},
	year = {2012},
	pages = {1125},
	abstract = {<p>In this paper, we study the limit, as ε goes to zero, of a particular solution of the equation $\epsilon^2A\ddot u^ε(t)+εB\dot u^ε(t)+\nabla_xf(t,u^ε(t))=0$, where $f(t,x)$ is a potential satisfying suitable coerciveness conditions. The limit $u(t)$ of $u^ε(t)$ is piece-wise continuous and verifies $\nabla_xf(t,u(t))=0$. Moreover, certain jump conditions characterize the behaviour of $u(t)$ at the discontinuity times. The same limit behaviour is obtained by considering a different approximation scheme based on time discretization and on the solutions of suitable autonomous systems.</p>},
	keywords = {discrete approximations, perturbation methods, saddle-node bifurcation, Singular perturbations, vanishing viscosity},
	issn = {1078-0947},
	doi = {10.3934/dcds.2012.32.1125},
	url = {http://aimsciences.org//article/id/560b82d9-f289-498a-a619-a4b132aaf9f8},
	author = {Virginia Agostiniani}
}
@article { ISI:000296627000002,
	title = {A MODEL FOR CRACK PROPAGATION BASED ON VISCOUS APPROXIMATION},
	journal = {{MATHEMATICAL MODELS \& METHODS IN APPLIED SCIENCES}},
	volume = {{21}},
	number = {{10}},
	year = {2011},
	month = {{OCT}},
	pages = {{2019-2047}},
	publisher = {{WORLD SCIENTIFIC PUBL CO PTE LTD}},
	type = {{Article}},
	address = {{5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE}},
	abstract = {<p>{In the setting of antiplane linearized elasticity, we show the existence of quasistatic evolutions of cracks in brittle materials by using a vanishing viscosity approach, thus taking into account local minimization. The main feature of our model is that the path followed by the crack need not be prescribed a priori: indeed, it is found as the limit (in the sense of Hausdorff convergence) of curves obtained by an incremental procedure. The result is based on a continuity property for the energy release rate in a suitable class of admissible cracks.}</p>},
	keywords = {Brittle fracture, Crack propagation, energy derivative, energy release rate, free-discontinuity problems, Griffith{\textquoteright}s criterion, local minimizers, stress intensity factor}, vanishing viscosity, {Variational models},
	issn = {{0218-2025}},
	doi = {{10.1142/S0218202511005647}},
	author = {Giuliano Lazzaroni and Rodica Toader}
}
