@article {DAVOLI2013615, title = {A quasistatic evolution model for perfectly plastic plates derived by Γ-convergence}, journal = {Annales de l{\textquoteright}Institut Henri Poincare (C) Non Linear Analysis}, volume = {30}, number = {4}, year = {2013}, pages = {615 - 660}, abstract = {

The subject of this paper is the rigorous derivation of a quasistatic evolution model for a linearly elastic{\textendash}perfectly plastic thin plate. As the thickness of the plate tends to zero, we prove via Γ-convergence techniques that solutions to the three-dimensional quasistatic evolution problem of Prandtl{\textendash}Reuss elastoplasticity converge to a quasistatic evolution of a suitable reduced model. In this limiting model the admissible displacements are of Kirchhoff{\textendash}Love type and the stretching and bending components of the stress are coupled through a plastic flow rule. Some equivalent formulations of the limiting problem in rate form are derived, together with some two-dimensional characterizations for suitable choices of the data.

}, keywords = {-convergence, Perfect plasticity, Prandtl{\textendash}Reuss plasticity, Quasistatic evolution, Rate-independent processes, Thin plates}, issn = {0294-1449}, doi = {https://doi.org/10.1016/j.anihpc.2012.11.001}, url = {http://www.sciencedirect.com/science/article/pii/S0294144912001035}, author = {Elisa Davoli and Maria Giovanna Mora} } @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} }