The effective energy of a lattice metamaterial
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915585794768896 |
|---|---|
| author | Li, Xuenan Kohn, Robert V. |
| author_facet | Li, Xuenan Kohn, Robert V. |
| contents | We study the sense in which the continuum limit of a broad class of discrete materials with periodic structures can be viewed as a nonlinear elastic material. While we are not the first to consider this question, our treatment is more general and more physical than those in the literature. Indeed, it applies to a broad class of systems, including ones that possess mechanisms; and we discuss how the degeneracy that plagues prior work in this area can be avoided by penalizing change of orientation. A key motivation for this work is its relevance to mechanism-based mechanical metamaterials. Such systems often have ``soft modes'', achieved in typical examples by modulating mechanisms. Our results permit the following more general definition of a soft mode: it is a macroscopic deformation whose effective energy vanishes -- in other words, one whose spatially-averaged elastic energy tends to zero in the continuum limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05436 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The effective energy of a lattice metamaterial Li, Xuenan Kohn, Robert V. Mathematical Physics 49N99, 74Q05, 74B20 We study the sense in which the continuum limit of a broad class of discrete materials with periodic structures can be viewed as a nonlinear elastic material. While we are not the first to consider this question, our treatment is more general and more physical than those in the literature. Indeed, it applies to a broad class of systems, including ones that possess mechanisms; and we discuss how the degeneracy that plagues prior work in this area can be avoided by penalizing change of orientation. A key motivation for this work is its relevance to mechanism-based mechanical metamaterials. Such systems often have ``soft modes'', achieved in typical examples by modulating mechanisms. Our results permit the following more general definition of a soft mode: it is a macroscopic deformation whose effective energy vanishes -- in other words, one whose spatially-averaged elastic energy tends to zero in the continuum limit. |
| title | The effective energy of a lattice metamaterial |
| topic | Mathematical Physics 49N99, 74Q05, 74B20 |
| url | https://arxiv.org/abs/2505.05436 |