Global injectivity in second-gradient Nonlinear Elasticity and its approximation with penalty terms

0508975 - ÚTIA 2020 RIV US eng J - Článek v odborném periodiku
Krömer, Stefan - Valdman, Jan
Global injectivity in second-gradient Nonlinear Elasticity and its approximation with penalty terms.
Mathematics and Mechanics of Solids. Roč. 24, č. 11 (2019), s. 3644-3673. ISSN 1081-2865. E-ISSN 1741-3028
Grant CEP: GA ČR GA18-03834S
Institucionální podpora: RVO:67985556
Klíčová slova: nonlinear elasticity * global injectivity * local injectivity * nonsimple materials * Ciarlet-Necas-condition * approximation
Obor OECD: Applied mathematics
Impakt faktor: 2.040, rok: 2019
Způsob publikování: Omezený přístup
http://library.utia.cas.cz/separaty/2019/MTR/kromer-0508975.pdf https://journals.sagepub.com/doi/10.1177/1081286519851554

We present a new penalty term approximating the Ciarlet-Nečas condition (global invertibility of deformations) as a soft constraint for hyperelastic materials. For non-simple materials including a suitable higher order term in the elastic energy, we prove that the penalized functionals converge to the original functional subject to the Ciarlet-Nečas condition. Moreover, the penalization can be chosen in such a way that for all low energy deformations, self-interpenetration is completely avoided already at all sufficiently small finite values of the penalization parameter. We also present numerical experiments in 2d illustrating our theoretical results.
Trvalý link: http://hdl.handle.net/11104/0299806