Γ -convergence Approximation of Fracture and Cavitation in Nonlinear Elasticity
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| 024 | 7 | 0 | |a 10.1007/s00205-014-0820-3 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-014-0820-3 | ||
| 245 | 0 | 0 | |a Γ -convergence Approximation of Fracture and Cavitation in Nonlinear Elasticity |h [Elektronische Daten] |c [Duvan Henao, Carlos Mora-Corral, Xianmin Xu] |
| 520 | 3 | |a Our starting point is a variational model in nonlinear elasticity that allows for cavitation and fracture that was introduced by Henao and Mora-Corral (Arch Rational Mech Anal 197:619-655, 2010). The total energy to minimize is the sum of the elastic energy plus the energy produced by crack and surface formation. It is a free discontinuity problem, since the crack set and the set of new surface are unknowns of the problem. The expression of the functional involves a volume integral and two surface integrals, and this fact makes the problem numerically intractable. In this paper we propose an approximation (in the sense of Γ-convergence) by functionals involving only volume integrals, which makes a numerical approximation by finite elements feasible. This approximation has some similarities to the Modica-Mortola approximation of the perimeter and the Ambrosio-Tortorelli approximation of the Mumford-Shah functional, but with the added difficulties typical of nonlinear elasticity, in which the deformation is assumed to be one-to-one and orientation-preserving. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2014 | ||
| 700 | 1 | |a Henao |D Duvan |u Faculty of Mathematics, Pontificia Universidad Católica de Chile, Vicuña Mackenna, 4860, Santiago, Chile |4 aut | |
| 700 | 1 | |a Mora-Corral |D Carlos |u Department of Mathematics, Faculty of Sciences, Universidad Autónoma de Madrid, 28049, Madrid, Spain |4 aut | |
| 700 | 1 | |a Xu |D Xianmin |u LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, NCMIS, Chinese Academy of Sciences, 100190, Beijing, China |4 aut | |
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 216/3(2015-06-01), 813-879 |x 0003-9527 |q 216:3<813 |1 2015 |2 216 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-014-0820-3 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-014-0820-3 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Henao |D Duvan |u Faculty of Mathematics, Pontificia Universidad Católica de Chile, Vicuña Mackenna, 4860, Santiago, Chile |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Mora-Corral |D Carlos |u Department of Mathematics, Faculty of Sciences, Universidad Autónoma de Madrid, 28049, Madrid, Spain |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Xu |D Xianmin |u LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, NCMIS, Chinese Academy of Sciences, 100190, Beijing, China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 216/3(2015-06-01), 813-879 |x 0003-9527 |q 216:3<813 |1 2015 |2 216 |o 205 | ||