%0 Thesis %D 2013 %T Minimality and stability results for a class of free-discontinuity and nonlocal isoperimetric problems %A Marco Bonacini %K free-discontinuity problems %I SISSA %G en %1 7204 %2 Mathematics %4 1 %# MAT/05 ANALISI MATEMATICA %$ Submitted by Marco Bonacini (mbonacin@sissa.it) on 2013-10-23T13:11:08Z No. of bitstreams: 1 bonacini_phd_thesis.pdf: 1472871 bytes, checksum: 5866ef2786cf6ae345bb61eba76361a7 (MD5) %] Introduction Chapter 1. Preliminaries Chapter 2. The Mumford-Shah functional Chapter 3. A variational model in epitaxial films theory Chapter 4. A nonlocal isoperimetric problem Bibliography %0 Journal Article %J {MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES} %D 2011 %T A MODEL FOR CRACK PROPAGATION BASED ON VISCOUS APPROXIMATION %A Giuliano Lazzaroni %A Rodica Toader %K Brittle fracture %K Crack propagation %K energy derivative %K energy release rate %K free-discontinuity problems %K Griffith's criterion %K local minimizers %K stress intensity factor} %K vanishing viscosity %K {Variational models %X

{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.}

%B {MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES} %I {WORLD SCIENTIFIC PUBL CO PTE LTD} %C {5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE} %V {21} %P {2019-2047} %8 {OCT} %G eng %9 {Article} %R {10.1142/S0218202511005647} %0 Journal Article %J {ANNALI DI MATEMATICA PURA ED APPLICATA} %D 2011 %T Quasistatic crack growth in finite elasticity with Lipschitz data %A Giuliano Lazzaroni %K Brittle fracture %K Crack propagation %K Energy minimization %K Finite elasticity %K free-discontinuity problems %K Griffith's criterion %K Non-interpenetration} %K Polyconvexity %K Quasistatic evolution %K Rate-independent processes %K {Variational models %X

{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.}

%B {ANNALI DI MATEMATICA PURA ED APPLICATA} %I {SPRINGER HEIDELBERG} %C {TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY} %V {190} %P {165-194} %8 {JAN} %G eng %9 {Article} %R {10.1007/s10231-010-0145-2}