Nonlinearity of Elastic Deformations and Moderateness of Strains as a Factor Explaining the Auxeticity of Materials

A theoretical attempt is proposed to explain the auxeticity of elastic materials by use of nonlinear models of elastic deformations for a wide range of strain values up to moderate level. Analytical expressions are obtained that correspond to three kinds of universal deformations (simple shear, uniaxial tension, omniaxial tension) within the framework of three models well-known in the nonlinear theory of elasticity: two-constant Neo-Hookean model, three-constant Mooney–Rivlin model, five-constant Murnaghan model. The most interesting novelty is that a sample of elastic material is deformed as a conventional material at small strains and as an auxetic at moderate strains.