Upper bounds for the homogenization problem in nonlinear elasticity: the incompressible case
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910454609084416 |
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| author | Ruf, Matthias Schäffner, Mathias |
| author_facet | Ruf, Matthias Schäffner, Mathias |
| contents | We consider periodic homogenization of hyperelastic models incorporating incompressible behavior via the constraint $\det(\nabla u)=1$. We show that the 'usual' homogenized integral functional $\int W_{\rm hom}(\nabla u)\,dx$, where $W_{\rm hom}$ is 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_12877 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Upper bounds for the homogenization problem in nonlinear elasticity: the incompressible case Ruf, Matthias Schäffner, Mathias Analysis of PDEs 49J45, 74B20, 74Q05 We consider periodic homogenization of hyperelastic models incorporating incompressible behavior via the constraint $\det(\nabla u)=1$. We show that the 'usual' homogenized integral functional $\int W_{\rm hom}(\nabla u)\,dx$, where $W_{\rm hom}$ is 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. |
| title | Upper bounds for the homogenization problem in nonlinear elasticity: the incompressible case |
| topic | Analysis of PDEs 49J45, 74B20, 74Q05 |
| url | https://arxiv.org/abs/2405.12877 |