<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Vavasis, Stephen</style></author><author><style face="normal" font="default" size="100%">Papoulia, Katerina</style></author><author><style face="normal" font="default" size="100%">Hirmand, M. Reza</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Second-order cone interior-point method for quasistatic and moderate dynamic cohesive fracture</style></title><secondary-title><style face="normal" font="default" size="100%">Comput. Meth. Appl.  Mech. Engr.</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2020</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://arxiv.org/abs/1909.10641</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">358</style></volume><pages><style face="normal" font="default" size="100%">112633</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;
	Second-order cone interior-point method for quasistatic and moderate dynamic cohesive fracture by S. Vavasis, &lt;a href=&quot;https://www.tesseraesolutions.com&quot;&gt;K. Papoulia&lt;/a&gt;, M. R. Hirmand
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	&amp;nbsp; Cohesive fracture is among the few techniques able to&lt;br&gt;&amp;nbsp; model complex fracture nucleation and propagation&lt;br&gt;&amp;nbsp; with a sharp (nonsmeared) representation&lt;br&gt;&amp;nbsp; of the crack.&amp;nbsp; Implicit time-stepping schemes are often favored&lt;br&gt;&amp;nbsp; in mechanics due to their ability to take larger time steps in&lt;br&gt;&amp;nbsp; quasistatic and moderate dynamic problems.&amp;nbsp; Furthermore,&lt;br&gt;&amp;nbsp; initially rigid cohesive models are typically preferred when&lt;br&gt;&amp;nbsp; the location of the crack is not known in advance, since&lt;br&gt;&amp;nbsp; initially elastic models artificially lower the material stiffness.&lt;br&gt;&amp;nbsp; It is challenging to include an initially rigid&lt;br&gt;&amp;nbsp; cohesive model in an implicit scheme because&lt;br&gt;&amp;nbsp; the initiation of fracture corresponds&lt;br&gt;&amp;nbsp; to a nondifferentiability of the underlying potential.&amp;nbsp; In&lt;br&gt;&amp;nbsp; this work, an interior-point method is proposed for implicit time&lt;br&gt;&amp;nbsp; stepping of initially rigid cohesive&lt;br&gt;&amp;nbsp; fracture.&amp;nbsp; It uses techniques developed for convex second-order&lt;br&gt;&amp;nbsp; cone programming for the nonconvex problem at hand.&amp;nbsp; The underlying cohesive model&lt;br&gt;&amp;nbsp; is taken from Papoulia (2017) and is based on a nondifferentiable&lt;br&gt;&amp;nbsp; energy function.&amp;nbsp; That previous work proposed an algorithm based on successive&lt;br&gt;&amp;nbsp; smooth approximations to the nondifferential objective for solving&lt;br&gt;&amp;nbsp; the resulting optimization problem.&amp;nbsp; It is argued herein that cone&lt;br&gt;&amp;nbsp; programming can capture the nondifferentiability without smoothing,&lt;br&gt;&amp;nbsp; and the resulting cone formulation is amenable to interior-point&lt;br&gt;&amp;nbsp; algorithms.&amp;nbsp; A further benefit of the formulation is that other&lt;br&gt;&amp;nbsp; conic inequality constraints are straightforward to incorporate.&lt;br&gt;&amp;nbsp; Computational results are provided showing that certain contact&lt;br&gt;&amp;nbsp; constraints can be easily handled and that the&lt;br&gt;&amp;nbsp; method is practical.
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</style></abstract><notes><style face="normal" font="default" size="100%">Arxiv version: &lt;a href=&quot;https://arxiv.org/abs/1909.10641&quot;&gt;https://arxiv.org/abs/1909.10641&lt;/a&gt;</style></notes></record></records></xml>