TY - JOUR T1 - A MODEL FOR CRACK PROPAGATION BASED ON VISCOUS APPROXIMATION JF - {MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES} Y1 - 2011 A1 - Giuliano Lazzaroni A1 - Rodica Toader KW - Brittle fracture KW - Crack propagation KW - energy derivative KW - energy release rate KW - free-discontinuity problems KW - Griffith's criterion KW - local minimizers KW - stress intensity factor} KW - vanishing viscosity KW - {Variational models AB -

{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.}

PB - {WORLD SCIENTIFIC PUBL CO PTE LTD} CY - {5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE} VL - {21} ER - TY - JOUR T1 - Quasistatic crack growth in finite elasticity with Lipschitz data JF - {ANNALI DI MATEMATICA PURA ED APPLICATA} Y1 - 2011 A1 - Giuliano Lazzaroni KW - Brittle fracture KW - Crack propagation KW - Energy minimization KW - Finite elasticity KW - free-discontinuity problems KW - Griffith's criterion KW - Non-interpenetration} KW - Polyconvexity KW - Quasistatic evolution KW - Rate-independent processes KW - {Variational models AB -

{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.}

PB - {SPRINGER HEIDELBERG} CY - {TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY} VL - {190} ER -