Conservative yet constitutively odd elasticity in prestressed metamaterials
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909803863867392 |
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| author | Engstrom, Tyler A. Sussman, Daniel M. |
| author_facet | Engstrom, Tyler A. Sussman, Daniel M. |
| contents | We introduce a design principle for mechanical metamaterials based on "odd elasticity, once removed." By revisiting classic results relating the variation of Cauchy stress and Lagrangian strain around a prestressed reference state, we show how anisotropic, equilibrium prestress can generate a major anti-symmetry in the material's constitutive response. Tuning the system to such a state drives it to a critical instability, radically transforming its acoustic properties. We then inverse-design several uniform 2D solids that act as unique waveguides supporting decoupled modes along special lattice directions: a string-like mode and an exotic, in-plane soft mode with a flexural character ($ω\sim q^2$). The soft modes are insensitive to the value of the anisotropic prestress and exhibit oscillating momentum density but support a non-oscillatory, constant energy current. This principle of harnessing conservative "oddness" to unlock instability-driven wave phenomena provides a powerful new route to creating tunable materials for filtering, guiding, and controlling mechanical waves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19560 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conservative yet constitutively odd elasticity in prestressed metamaterials Engstrom, Tyler A. Sussman, Daniel M. Soft Condensed Matter We introduce a design principle for mechanical metamaterials based on "odd elasticity, once removed." By revisiting classic results relating the variation of Cauchy stress and Lagrangian strain around a prestressed reference state, we show how anisotropic, equilibrium prestress can generate a major anti-symmetry in the material's constitutive response. Tuning the system to such a state drives it to a critical instability, radically transforming its acoustic properties. We then inverse-design several uniform 2D solids that act as unique waveguides supporting decoupled modes along special lattice directions: a string-like mode and an exotic, in-plane soft mode with a flexural character ($ω\sim q^2$). The soft modes are insensitive to the value of the anisotropic prestress and exhibit oscillating momentum density but support a non-oscillatory, constant energy current. This principle of harnessing conservative "oddness" to unlock instability-driven wave phenomena provides a powerful new route to creating tunable materials for filtering, guiding, and controlling mechanical waves. |
| title | Conservative yet constitutively odd elasticity in prestressed metamaterials |
| topic | Soft Condensed Matter |
| url | https://arxiv.org/abs/2509.19560 |