TensND.jl

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References ​

Works cited in this documentation. Every entry has been checked against Crossref — DOI, authors, journal, volume, issue, pages and year — or, for the books without a DOI, against the publisher record.

The documentation follows one rule throughout: every formula is either accompanied by a citation, derived explicitly on the page from expressions that are, or read off the implementation with the source file named. Where a convention differs between references, the competing conventions are named and the one implemented by TensND is stated.

  1. W. Thomson. Elements of a mathematical theory of elasticity. Philosophical Transactions of the Royal Society of London 146, 481–498 (1856).

  2. J. Mandel. Généralisation de la théorie de plasticité de W. T. Koiter. International Journal of Solids and Structures 1, 273–295 (1965).

  3. M. M. Mehrabadi and S. C. Cowin. Eigentensors of linear anisotropic elastic materials. The Quarterly Journal of Mechanics and Applied Mathematics 43, 15–41 (1990).

  4. M. Bornert, T. Bretheau and P. Gilormini. Homogénéisation en mécanique des matériaux (Hermès Science, Paris, 2001).

  5. L. Morin, P. Gilormini and K. Derrien. Generalized Euclidean distances for elasticity tensors. Journal of Elasticity 138, 221–232 (2020).

  6. L. J. Walpole. Fourth-rank tensors of the thirty-two crystal classes: multiplication tables. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 391, 149–179 (1984).

  7. L. J. Walpole. Elastic behavior of composite materials: theoretical foundations. Advances in Applied Mechanics 21, 169–242 (1981).

  8. A. Hoenig. The behavior of a flat elliptical crack in an anisotropic elastic body. International Journal of Solids and Structures 14, 925–934 (1978).

  9. A. Hoenig. Elastic moduli of a non-randomly cracked body. International Journal of Solids and Structures 15, 137–154 (1979).

  10. M. Moakher and A. N. Norris. The closest elastic tensor of arbitrary symmetry to an elasticity tensor of lower symmetry. Journal of Elasticity 85, 215–263 (2006).

  11. J. T. Browaeys and S. Chevrot. Decomposition of the elastic tensor and geophysical applications. Geophysical Journal International 159, 667–678 (2004).

  12. J. G. Simmonds. A Brief on Tensor Analysis. 2nd Edition, Undergraduate Texts in Mathematics (Springer, New York, 1994).

  13. T. Mura. Micromechanics of Defects in Solids. 2nd Edition (Springer Netherlands, Dordrecht, 1987).