Hyperelastic behaviour of auxetic material in tension and compression tests

Małgorzata Janus-Michalska


This paper presents the numerical simulation of uniaxial tension and compression tests for negative Poisson’s ratio materials subjected to large strains. Numerical calculations are performed for the determination of the material characteristics of auxetic periodic lattices. The finite element method (FEM) coupled with 2D periodic homogenisation technique is used. The results show the existence of large variations in strain-stress plots, which can be achieved by changing the lattice geometry parameters.

Słowa kluczowe: auxetic microstructure, hyperelasticity, material characteristics

[1] Alderson A., Alderson K.L., Auxetic materials,Proceedingsof the Institution of Mechanical Engineers, Part G, Journal of Aerospace Engineering – Special Issue Paper, 2007, 565–575.

 [2] Alderson K.L., Alderson A., Evans K.E., The Interpretation of the Strain–dependent Poisson’s Ratio in Auxetic Polyethylene,J. Strain Anal., 1998, 32, 201– 212.

 [3]   Danielsson M., Parks D., Boyce M.C., Constitutive modelling of porous hyperelastic materials, Mechanics of Materials, 2004, 36, 347–358.

[4]    Darijani H., Naghdabadi R., Hyperelastic materials behavior modeling using consistent strain energy density functions,Acta Mechanica, 2010, 213, 235–254.

 [5] Dirrenberger J., Forest S., Jeulin D., Colin C., Homogenization of periodic auxetic materials,Procedia Engineering 10, 2011, 1847–1852.

 [6]   Dłużewski P., Anisotropic Hyperelasticity Based Upon General Strain Measures,Journal of Elasticity, 60, 2000, 119–129.

[7]    Federico S., Grillo A., Imatani S., Giaquinta G., Herzog W., An energetic approach to the analysis of anisotropic hyperelastic materials, International Journal of Engineering Science, 46, 2008, 164–181.

[8] Greaves G.N., Greer A.L., Lakes R.S., Rouxel T., Poisson’s ratio and modern materials, Modern Materials, Published online, review article, 24 October 2011, DOI: 10.1038 NMAT 3134.

[9] Holzeapfel G.A., Nonlinear Solid Mechanics,A Continuum Approach for Engineering, Technical University, Graz, Austria 2000.

[10]  Horgan C., The remarkable Gent constitutive model for hyperelastic materials,International Journal of Non–Linear Mechanics, 68, 2015, 9–16.

[11] Janus-Michalska M., Hyperelastic behavior of cellular structures based on micromechanical modeling at small strain, Archives of Mechanics, Issue 1, Vol. 63, Warszawa 2011, 3–24.

[12] Janus-Michalska M., Micromechanical Model of Auxetic Cellular Materials, Issue 4, Vol. 47, Journal of Theoretical and Applied Mechanics, 2009,5–22.

 [13] Janus-Michalska M., Effective Model Describing Elastic Behaviour of Cellular Materials,Archives of Metallurgy and Materials, Vol. 50/3, 2005, 595–608.

[14] Kumar R.S., McDowell D.L., Generalized Continuum Modelling of 2–D periodic Cellular Solids,Int. Journal of Solids and Structures, 41, 7299–7422.

[15 ] Murphy G.J., Strain Energy Functions for a Poisson Power Law Function in Simple Tension of Compressible Hyperelastic Materials, Journal of Elasticity, 60, 2000, 151–164.

[16] Nemat-Maser S., Hori M., Micromechanics,2nd Edition, Elsevier, 1999.

[17] Smith C.W., Wootton R.J., Evans K.E., Interpretation of experimental data for Poisson’s ratio of highly nonlinear materials energy density functions, Acta Mechanica, 213, 2010, 235–254.

[18]  Vegori L., Destrade M., McGarry P., Ogden R., On anisotropic elasticity and questions concerning its FiniteElement implementation, Computational Mechanics, 52, 2013, 1185–1197.

[19]  Wang F., Sigmund O., Jensen J.S., Design of materials with prescribed nonlinear properties, Journal of mechanics and Physics of Solids, 69, 2014, 156–174.