Upper bounds for the homogenization problem in nonlinear elasticity: the incompressible case
- We consider periodic homogenization of hyperelastic models incorporating incompressible behavior via the constraint det(∇u)=1. We show that the ’usual’ homogenized integral functional ∫Whom(∇u)dx, where Whomis the standard multicell-formula of non-convex homogenization restricted to volume preserving deformations, yields an upper bound for the Γ-limit as the scale of periodicity tends to zero.
| Author: | Matthias RufORCiDGND, Mathias Schäffner |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1137287 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/113728 |
| ISSN: | 0944-2669OPAC |
| ISSN: | 1432-0835OPAC |
| Parent Title (English): | Calculus of Variations and Partial Differential Equations |
| Publisher: | Springer |
| Place of publication: | Berlin |
| Type: | Article |
| Language: | English |
| Date of Publication (online): | 2024/06/28 |
| Year of first Publication: | 2026 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2024/07/01 |
| Volume: | 65 |
| Issue: | 1 |
| First Page: | 4 |
| DOI: | https://doi.org/10.1007/s00526-025-03177-1 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Nichtlineare Analysis | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY 4.0: Creative Commons: Namensnennung |
