01532nas a2200277 4500008004100000022001600041245006500057210006300122260009400185300001600279490000900295520056700304653002100871653002200892653002200914653002400936653003200960653002500992653002101017653002901038653002401067653002401091100002401115700001901139856009601158 2011 eng d a{0218-2025}00aA MODEL FOR CRACK PROPAGATION BASED ON VISCOUS APPROXIMATION0 aMODEL FOR CRACK PROPAGATION BASED ON VISCOUS APPROXIMATION a{5 TOH TUCK LINK, SINGAPORE 596224, SINGAPORE}b{WORLD SCIENTIFIC PUBL CO PTE LTD}c{OCT} a{2019-2047}0 v{21}3 a
{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.}
10aBrittle fracture10aCrack propagation10aenergy derivative10aenergy release rate10afree-discontinuity problems10aGriffith's criterion10alocal minimizers10astress intensity factor}10avanishing viscosity10a{Variational models1 aLazzaroni, Giuliano1 aToader, Rodica uhttps://www.math.sissa.it/publication/model-crack-propagation-based-viscous-approximation-001263nas a2200277 4500008004100000022001600041245007000057210006900127260008600196300001400282490001000296520028400306653002100590653002200611653002400633653002200657653003200679653002500711653002600736653001800762653002600780653003100806653002400837100002400861856010000885 2011 eng d a{0373-3114}00aQuasistatic crack growth in finite elasticity with Lipschitz data0 aQuasistatic crack growth in finite elasticity with Lipschitz dat a{TIERGARTENSTRASSE 17, D-69121 HEIDELBERG, GERMANY}b{SPRINGER HEIDELBERG}c{JAN} a{165-194}0 v{190}3 a{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.}
10aBrittle fracture10aCrack propagation10aEnergy minimization10aFinite elasticity10afree-discontinuity problems10aGriffith's criterion10aNon-interpenetration}10aPolyconvexity10aQuasistatic evolution10aRate-independent processes10a{Variational models1 aLazzaroni, Giuliano uhttps://www.math.sissa.it/publication/quasistatic-crack-growth-finite-elasticity-lipschitz-data