The elastic constants of an isotropic medium can have arbitrary values

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Abstract

Using the example of the matrix of elastic constants of an isotropic material, it is shown that the Young’s modulus, shear modulus, volume modulus, and Poisson’s ratio can take any real values. In this case, the positive definiteness of the matrix of elastic constants is not mandatory, as is traditionally assumed. The positivity of the specific strain energy also occurs when the matrix of elastic constants is not positive definite. It is sufficient for the invertibility of the relations of Hooke’s law to require the non-degeneracy of the matrix of elasticity constants. Graphs of Young’s modules, volume and Poisson’s ratio depending on the ratio of Lame constants are given.

About the authors

N. I. Ostrosablin

Institute of Hydrodynamics named after M.A. Lavrentiev, Siberian Branch of the Russian Academy of Sciences

Email: o.n.ii@yandex.ru
Novosibirsk, Russia

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