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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/2509.16907 |
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| _version_ | 1866917066630496256 |
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| author | Li, Xuenan Kohn, Robert V. |
| author_facet | Li, Xuenan Kohn, Robert V. |
| contents | There is a growing mechanics literature concerning the macroscopic properties of mechanism-based mechanical metamaterials. This amounts mathematically to a homogenization problem involving nonlinear elasticity. A key goal is to identify the "soft modes" of the metamaterial. We achieve this goal using methods from homogenization for some specific 2D examples -- including discrete models of the Rotating Squares metamaterial and the Kagome metamaterial -- whose soft modes are compressive conformal maps. The innovation behind this achievement is a new technique for bounding the effective energy from below, which takes advantage of the metamaterial's structure and symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16907 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A nonlinear homogenization-based perspective on the soft modes and effective energies of some conformal metamaterials Li, Xuenan Kohn, Robert V. Analysis of PDEs Mathematical Physics 49Nxx There is a growing mechanics literature concerning the macroscopic properties of mechanism-based mechanical metamaterials. This amounts mathematically to a homogenization problem involving nonlinear elasticity. A key goal is to identify the "soft modes" of the metamaterial. We achieve this goal using methods from homogenization for some specific 2D examples -- including discrete models of the Rotating Squares metamaterial and the Kagome metamaterial -- whose soft modes are compressive conformal maps. The innovation behind this achievement is a new technique for bounding the effective energy from below, which takes advantage of the metamaterial's structure and symmetry. |
| title | A nonlinear homogenization-based perspective on the soft modes and effective energies of some conformal metamaterials |
| topic | Analysis of PDEs Mathematical Physics 49Nxx |
| url | https://arxiv.org/abs/2509.16907 |