To modeling the auxetic materials: some fundamental aspects

Rushchitsky J. J.
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The auxetic materials are considered from the point of view of correspondence to the classical theory of elasticity. It is shown that some classical postulates relative to the elastic constants should be refined. Three cases of description of auxetic materials — by the model of linear elastic isotropic body, by the model of linear elastic transversally isotropic body, by the nonlinear elastic isotropic body (Murnaghan potential) — are analyzed shortly. The initial assumption on positivity of internal energy of deformation is saved and then the uniform stress states (unilateral tension, omnilateral compression, pure shear) are used to analyze the elastic constants. This allows to describe the new mechanical effects: expansion of the standard sample-rod-prism under unilateral tension and expansion of the standard sample-cube under hydrostatic compression as well as an existence of the arbitrary negative values of Poisson ratios, what is accompanied by the negative values of the Lame $\lambda$, Young $E$ and compression $k$ moduli, for the linear isotropic case and some elastic constants in the linear transversely isotropic case. The case of nonlinear description shows that the auxetic materials should be defined by the primary physical effect — observation in the standard for mechanics of materials experiment of longitudinal tension of a prism that the transverse deformation of prism is positive (a material as if swells) in contrast to the classical materials, where it is negative.
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Math. Model. Comput. Vol.1, No.1, pp.97-108 (2014)