Linear Algebra Provides a Basis for Elasticity without Stress or Strain

H. H. Hardy^{*}

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References

[1] [1] Todhunter, I. (1886) A History of the Theory of Elasticity and of the Strength of Materials from Galilei to the Present Time. Cambridge University Press, Cambridge.

[2] [2] Spencer, A.J. (1980) Continuum Mechanics. Dover, New York.

[3] [3] Rivlin, R.S. and Saunders, D.W. (1951) Large Elastic Deformations of Isotropic Materials. VII. Experiments on the Deformation of Rubber. Philosophical Transactions of the Royal Society of London. Series A. Mathematical and Physical Sciences, 243, 251-288. http://dx.doi.org/10.1098/rsta.1951.0004

[4] [4] Hardy, H.H. and Shmidheiser, H. (2011) A Discrete Region Model of Isotropic Elasticity. Mathematics and Mechanics of Solids, 16, 317-333. http://dx.doi.org/10.1177/1081286510391666

[5] [5] Hardy, H.H. (2013) Euler-Lagrange Elasticity: Differential Equation for Elasticity without Stress or Strain. Journal of Applied Mathematics and Physics, 1, 26-30. http://dx.doi.org/10.4236/jamp.2013.17004

[6] [6] Gilbert, J.D. (1970) Elements of Linear Algebra. International Textbook Company, Scranton.

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[8] [8] Landau, L.D. and Lifshitz, E.M. (2005) Theory of Elasticity, Course of Theoretical Physics. Volume 7, Elsevier, London.

[9] [9] Hardy, H.H. (2014) Euler-Lagrange Elasticity with Dynamics. Journal of Applied Mathematics and Physics, 2, 1183-1189. http://dx.doi.org/10.4236/jamp.2014.213138

[10] [10] Truesdale, C. and Noll, W. (2004) The Non-Linear Field Theories of Mechanics. Springer-Verlag, New York.
http://dx.doi.org/10.1007/978-3-662-10388-3

[11] [11] Wu, H.-C. (2004) Continuum Mechanics and Plasticity. CRC Press, New York.
http://dx.doi.org/10.1201/9780203491997

[12] [12] Kelly, P. (2015) Mechanics Lecture Notes Part III: Foundations of Continuum Mechanics.
http://homepages.engineering.auckland.ac.nz/~pkel015/SolidMechanicsBooks/Part_III/