@article {Lazzaroni2018, title = {On the Quasistatic Limit of Dynamic Evolutions for a Peeling Test in Dimension One}, journal = {Journal of Nonlinear Science}, volume = {28}, number = {1}, year = {2018}, month = {Feb}, pages = {269{\textendash}304}, abstract = {

The aim of this paper is to study the quasistatic limit of a one-dimensional model of dynamic debonding. We start from a dynamic problem that strongly couples the wave equation in a time-dependent domain with Griffith{\textquoteright}s criterion for the evolution of the domain. Passing to the limit as inertia tends to zero, we find that the limit evolution satisfies a stability condition; however, the activation rule in Griffith{\textquoteright}s (quasistatic) criterion does not hold in general, thus the limit evolution is not rate-independent.

}, issn = {1432-1467}, doi = {10.1007/s00332-017-9407-0}, url = {https://doi.org/10.1007/s00332-017-9407-0}, author = {Giuliano Lazzaroni and Lorenzo Nardini} } @article {Crismale2017, title = {Quasistatic crack growth based on viscous approximation: a model with branching and kinking}, journal = {Nonlinear Differential Equations and Applications NoDEA}, volume = {24}, number = {1}, year = {2017}, month = {Jan}, pages = {7}, abstract = {

Employing the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions of cracks in brittle materials in the setting of antiplane shear. The crack path is not prescribed a priori and is chosen in an admissible class of piecewise regular sets that allows for branching and kinking.

}, issn = {1420-9004}, doi = {10.1007/s00030-016-0426-6}, url = {https://doi.org/10.1007/s00030-016-0426-6}, author = {Vito Crismale and Giuliano Lazzaroni} } @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} } @article {2010, title = {Quasistatic crack growth in finite elasticity with non-interpenetration}, journal = {Ann. Inst. H. Poincare Anal. Non Lineaire 27 (2010) 257-290}, number = {SISSA;80/2008/M}, year = {2010}, abstract = {

We present a variational model to study the quasistatic growth of brittle cracks in hyperelastic materials, in the framework of finite elasticity, taking\\ninto account the non-interpenetration condition.

}, doi = {10.1016/j.anihpc.2009.09.006}, url = {http://hdl.handle.net/1963/3397}, author = {Gianni Dal Maso and Giuliano Lazzaroni} }