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Which Elasticity Tensors are Realizable?
Abstract
It is shown that any given positive definite fourth order tensor satisfying the usual symmetries of elasticity tensors can be realized as the effective elasticity tensor of a two-phase composite comprised of a sufficiently compliant isotropic phase and a sufficiently rigid isotropic phase configured in an suitable microstructure. The building blocks for constructing this composite are what we call extremal materials. These are composites of the two phases which are extremely stiff to a set of arbitrary given stresses and, at the same time, are extremely compliant to any orthogonal stress. An appropriately chosen subset of the extremal materials are layered together to form the composite with elasticity tensor matching the given tensor.
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Citations
Cited by
Flexible mechanical metamaterials
Bertoldi, K., Vitelli, V., Christensen, J., & van Hecke, M. (2017) · Nature Reviews Materials · doi:10.1038/natrevmats.2017.66 · Cited by 1,867
An elasto-mechanical unfeelability cloak made of pentamode metamaterials
Bückmann, T., Thiel, M., Kadic, M., Schittny, R., & Wegener, M. (2014) · Nature Communications · doi:10.1038/ncomms5130 · Cited by 623
Programmable Self‐Locking Origami Mechanical Metamaterials
Fang, H., Chu, S. A., Xia, Y., & Wang, K. (2018) · Advanced Materials · doi:10.1002/adma.201706311 · Cited by 328
Metadata
- Authors
- Milton, G. W., & Cherkaev, A. V.
- Venue
- Journal of Engineering Materials and Technology
- Publisher
- ASME International
- Published
- 1995-10-01
- Volume
- 117
- Issue
- 4
- Pages
- 483-493
- ISSN
- 0094-4289 (ISSN-L)
- 1528-8889
- OpenAlex
- W1999864615
- Cited by
- 513
- References
- 0
- FWCI
- 2.88
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Which Elasticity Tensors are Realizable? https://app.cochat.ai/papers/10.1115/1.2804743
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- Milton, G. W., & Cherkaev, A. V. (1995). Which Elasticity Tensors are Realizable? Journal of Engineering Materials and Technology. https://doi.org/10.1115/1.2804743
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
