0552275 20250310145740.420220124235959.9 85122069400 000736720500001 10.1007/s00332-021-09769-3 26 s. P cav_un_epca*02539370938-897432Springer crack gradient polyconvexity calculus of variations cav_un_auth*0101142 Kružík Martin UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0422841 Mariano P. M. IT 33 K cav_un_auth*0422840 Mucci D. IT 33 http://library.utia.cas.cz/separaty/2022/MTR/kruzik-0552275.pdf https://link.springer.com/article/10.1007/s00332-021-09769-3 GF19-29646L GA ČR CZ cav_un_auth*0385134 In a set of infinitely many reference configurations differing from a chosen fit region B in the three-dimensional space and from each other only by possible crack paths, a set parameterized by special measures, namely curvature varifolds, energy minimality selects among possible configurations of a continuous body those that are compatible with assigned boundary conditions of Dirichlet-type. The use of varifolds allows us to consider both “material phase” (cracked or non-cracked) and crack orientation. The energy considered is gradient polyconvex: it accounts for relative variations of second- neighbor surfaces and pressure-confinement effects. We prove existence of minimizers for such an energy. They are pairs of deformations and curvature varifolds. The former ones are taken to be SBV maps satisfying an impenetrability condition. Their jump set is constrained to be in the varifold support. WOS CE 10000 10100 10102 2022 3 2 R hod 4 4rh 4 20250310145726.9 4 20250310145740.4 RVO:67985556 http://hdl.handle.net/11104/0327547 1 S 16 3+4 Article Mathematics Applied|Mechanics|Physics Mathematical C PHYSICS.MATHEMATICAL|MECHANICS|MATHEMATICS.APPLIED 3 0.7 6 0.00554 1.516 2672 1.35 2.900 98 Q1 81 Q1* Q1 1.16 Q1 91.6 2022 Soubory v repozitáři: kruzik-552275.pdf 85122069400 SCOPUS PUBMED 000736720500001 WOS cav_un_epca*0253937 Journal of Nonlinear Science 0938-8974 1432-1467 Roč. 32 č. 1 2022 Springer