2023/02/13 by Stefan Krömer, Krömer, Stefan, Jan Valdman +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #35Q74 (Secondary) #49N99 (Primary) 65Z05 #Analysis of PDEs (math.AP) #Cellular Mechanics and Interactions #Contact Mechanics and Variational Inequalities #Elasticity and Material Modeling #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2302.06268
openalex publication_date 2023/02/13 · openalex created_date 2023/02/16 · openalex updated_date 2026/07/28
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.