@mastersthesis {2013, title = {Minimality and stability results for a class of free-discontinuity and nonlocal isoperimetric problems}, year = {2013}, school = {SISSA}, keywords = {free-discontinuity problems}, author = {Marco Bonacini} } @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 = {

{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.}

}, 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} } @article { ISI:000286300100012, title = {Quasistatic crack growth in finite elasticity with Lipschitz data}, journal = {{ANNALI DI MATEMATICA PURA ED APPLICATA}}, volume = {{190}}, number = {{1}}, year = {2011}, month = {{JAN}}, pages = {{165-194}}, publisher = {{SPRINGER HEIDELBERG}}, type = {{Article}}, address = {{TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY}}, abstract = {

{We extend the recent existence result of Dal Maso and Lazzaroni (Ann Inst H Poincare Anal Non Lineaire 27:257-290, 2010) for quasistatic evolutions of cracks in finite elasticity, allowing for boundary conditions and external forces with discontinuous first derivatives.}

}, keywords = {Brittle fracture, Crack propagation, Energy minimization, Finite elasticity, free-discontinuity problems, Griffith{\textquoteright}s criterion, Non-interpenetration}, Polyconvexity, Quasistatic evolution, Rate-independent processes, {Variational models}, issn = {{0373-3114}}, doi = {{10.1007/s10231-010-0145-2}}, author = {Giuliano Lazzaroni} }