A homogenization result in finite plasticity
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910356390019072 |
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| author | Davoli, Elisa Gavioli, Chiara Pagliari, Valerio |
| author_facet | Davoli, Elisa Gavioli, Chiara Pagliari, Valerio |
| contents | We carry out a variational study for integral functionals that model the stored energy of a heterogeneous material governed by finite-strain elastoplasticity with hardening. Assuming that the composite has a periodic microscopic structure, we establish the $Γ$-convergence of the energies in the limiting of vanishing periodicity. The constraint that plastic deformations belong to $\mathsf{SL}(3)$ poses the biggest hurdle to the analysis, and we address it by regarding $\mathsf{SL}(3)$ as a Finsler manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_09084 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A homogenization result in finite plasticity Davoli, Elisa Gavioli, Chiara Pagliari, Valerio Analysis of PDEs 49J45, 74C15, 74E30, 74Q05 We carry out a variational study for integral functionals that model the stored energy of a heterogeneous material governed by finite-strain elastoplasticity with hardening. Assuming that the composite has a periodic microscopic structure, we establish the $Γ$-convergence of the energies in the limiting of vanishing periodicity. The constraint that plastic deformations belong to $\mathsf{SL}(3)$ poses the biggest hurdle to the analysis, and we address it by regarding $\mathsf{SL}(3)$ as a Finsler manifold. |
| title | A homogenization result in finite plasticity |
| topic | Analysis of PDEs 49J45, 74C15, 74E30, 74Q05 |
| url | https://arxiv.org/abs/2204.09084 |