A continuum hyperelastic model for auxetic materials

Abstract

We propose a simple mathematical model to describe isotropic auxetic materials in the framework of the classical theory of nonlinear elasticity. The model is derived from the Blatz-Ko constitutive equation for compressible foams and makes use of a nonmonotonic Poisson function. An application to the modelling of auxetic foams is considered and it is shown that the material behaviour is adequately described with only three constitutive parameters.

Manufacturing, characteristics and applications of auxetic foams: A state-of-the-art review

“…Lakes et al also introduced Cosserat (micropolar) theory [174] for the analysis of materials with negative Poisson's ratios [108,175,176], stating that syntactic foams could be regarded as classical ones apart from small deviations. Rueger and Lakes however found compelling experimental evidence of the existence of Cosserat torsion lengths and coupling due to size effects while testing the foams [177].…”

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

“…A prevalent majority of scientists identify up to this time auxeticity with negativity of Poisson/s ratio. A few publications only exist, where the nonlinear models are used (for example, [39] and experiments with large strains in auxetics (for example, [4,9,43,45]).…”

“…Apply further to the nonlinear equations ( 36) - (38) the procedure of analysis of the state of uniaxial tension that is used in the linear theory of elasticity as applied to equations (39). Sub traction of equation (38) from equation (37) gives the formula…”

Finite deformation and fractional order viscoelasticity of an auxetic foam

“…In most model development, multi-axial deformation over nonlinear regimes has not been extensively evaluated which presents challenges when developing models that can accommodate large deformation often encountered in polymeric foam applications. Previous work describing the behavior of auxetic materials was largely based on the Blatz-Ko model (Ciambella and Saccomandi, 2014). The Blatz-Ko model was initially considered in the work presented here but it was limited in its ability to predict nonlinear auxetic material behavior in finite deformation regimes where the auxetic foam ribs straighten out and the Poisson’s ratio becomes positive.…”