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Bibliografie

Journal Article

Surface penalization of self-interpenetration in linear and nonlinear elasticity

Krömer Stefan, Valdman Jan

: Applied Mathematical Modelling vol.122, 1 (2023), p. 641-664

: GF21-06569K, GA ČR

: Elasticity, Global injectivity and self-contact, Locking constraints, Nonsimple materials, Ciarlet-Nečas-condition, Approximation

: 10.1016/j.apm.2023.06.018

: http://library.utia.cas.cz/separaty/2023/MTR/kromer-0575785-preprint.pdf

: https://www.sciencedirect.com/science/article/pii/S0307904X23002731?via%3Dihub

(eng): We analyze a term penalizing surface self-penetration, as a soft constraint for models of hyperelastic materials to approximate the Ciarlet-Nečas condition (almost everywhere global invertibility of deformations). For a linear elastic energy subject to an additional local invertibility constraint, we prove that the penalized elastic functionals converge to the original functional subject to the Ciarlet-Nečas condition. The approach also works for nonlinear models of non-simple materials including a suitable higher order term in the elastic energy, without artificial local constraints. Numerical experiments illustrate our results for a self-contact problem in 3d.

: BA

: 10102