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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.00630 |
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| _version_ | 1866918077867753472 |
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| author | Audoly, Basile Lestringant, Claire Nassar, Hussein |
| author_facet | Audoly, Basile Lestringant, Claire Nassar, Hussein |
| contents | We propose a methodology for the homogenization of periodic elastic lattices that covers the case of unstable lattices, having affine (macroscopic) or periodic (microscopic) mechanisms. The singular cell problems that are encountered when a periodic mechanism is present are naturally solved by treating the amplitude $θ(X)$ of the mechanism as an enrichment variable. We use asymptotic second-order homogenization to derive an effective energy capturing both the strain-gradient effect $\nabla \varepsilon$ relevant to affine mechanisms, and the $\nabla θ$ regularization relevant to periodic mechanisms, if any is present. The proposed approach is illustrated with a selection of lattices displaying a variety of effective behaviors. It follows a unified pattern that leads to a classification of these effective behaviors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00630 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classifying soft elastic lattices using higher-order homogenization Audoly, Basile Lestringant, Claire Nassar, Hussein Soft Condensed Matter We propose a methodology for the homogenization of periodic elastic lattices that covers the case of unstable lattices, having affine (macroscopic) or periodic (microscopic) mechanisms. The singular cell problems that are encountered when a periodic mechanism is present are naturally solved by treating the amplitude $θ(X)$ of the mechanism as an enrichment variable. We use asymptotic second-order homogenization to derive an effective energy capturing both the strain-gradient effect $\nabla \varepsilon$ relevant to affine mechanisms, and the $\nabla θ$ regularization relevant to periodic mechanisms, if any is present. The proposed approach is illustrated with a selection of lattices displaying a variety of effective behaviors. It follows a unified pattern that leads to a classification of these effective behaviors. |
| title | Classifying soft elastic lattices using higher-order homogenization |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/2507.00630 |