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Mathematical Foundations of Elasticity
Abstract
This advanced-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It is directed to mathematicians, engineers and physicists who wish to see this classical subject in a modern setting with examples of newer mathematical contributions. Prerequisites include a solid background in advanced calculus and the basics of geometry and functional analysis.The first two chapters cover the background geometry ― developed as needed ― and use this discussion to obtain the basic results on kinematics and dynamics of con
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Cited by
Hill, D. L. G., Batchelor, P. G., Holden, M., & Hawkes, D. J. (2001) · Physics in Medicine and Biology · doi:10.1088/0031-9155/46/3/201 · Cited by 2,093
Simo, J. C. (1987) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(87)90107-1 · Cited by 1,063
The Euler–Poincaré Equations and Semidirect Products with Applications to Continuum Theories
Holm, D. D., Marsden, J. E., & Ratiu, T. S. (1998) · Advances in Mathematics · doi:10.1006/aima.1998.1721 · Cited by 964
Self-citationFinite element implementation of incompressible, transversely isotropic hyperelasticity
Weiss, J. A., Maker, B. N., & Govindjee, S. (1996) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(96)01035-3 · Cited by 797
Simo, J. C., & Ortiz, M. (1985) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/0045-7825(85)90061-1 · Cited by 658
Metadata
- Authors
- Marsden, J. E., Hughes, T. J. R., & Carlson, D. E.
- Venue
- Journal of Applied Mechanics
- Publisher
- ASME International
- Published
- 1984-12-01
- Volume
- 51
- Issue
- 4
- Pages
- 946-946
- ISSN
- 0021-8936 (ISSN-L)
- 1528-9036
- OpenAlex
- W2065668980
- Cited by
- 2,665
- References
- 0
- FWCI
- 48.98
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Mathematical Foundations of Elasticity. https://app.cochat.ai/papers/10.1115/1.3167757
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- Marsden, J. E., Hughes, T. J. R., & Carlson, D. E. (1984). Mathematical Foundations of Elasticity. Journal of Applied Mechanics. https://doi.org/10.1115/1.3167757
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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.
