Advances in Engineering Advances in Engineering features breaking research judged by Advances in Engineering advisory team to be of key importance in the Engineering field. Papers are selected from over 10,000 published each week from most peer reviewed journals.
Significance Statement
Auxetic materials have a unique feature: when subjected to simple tension, they undergo lateral expansion and lateral compression when compressed. This behaviour is exactly the opposite one would expect when testing standard materials. Owing to their perculiarity, they are widely used as structural components in aerospace and civil applications.
We present for the first time a theoretical framework to model these materials within the classical theory of continuum nonlinear elasticity.
Despite its simplicity, the model we propose is feasible for a direct application in a finite element code and it is based on three constitutive parameters easily identifiable from the experiments: the shear modulus, the infinitesimal Poisson’s ratio and the lateral stretch at inversion. The comparison of the model with experimental data confirms a good qualitative agreement with real world materials. This situation is interesting for several reasons. First of all we have a mathematical tool to investigate in a simple and direct way the mechanics of auxetic materials at finite strains. Second, the model may be implemented directly in any commercial finite element software. All this in contrast with complex microstructural based models that may investigated only via ad-hoc numerical simulations highly dependent on the specific framework of investigation.
It is clear that the model may be refined in several directions, but its qualitative agreement with the experimental data with only 3 constitutive parameters is remarkable. We are able to describe the main features of the Poisson function for auxetic materials, and to describe stress and strain data over the range of finite strains relevant to the applications.
For all these reasons, we think that it is worth to investigate further this model in various technical applications of auxetic foams where finite deformations cannot be neglected. On the other hand, more refined models could be considered by using a different expression of the strain energy function. This is to describe second order effects of auxetic foams that may be of a certain interest in specific applications.
We further point out that the procedure we have followed to derive the constitutive model can be generalised to anisotropic materials with the proper choice of the strain energy function. This would allow the description of other type of auxetic foams which cannot be considered isotropic due to the inherent nature of their microstructure.
Journal Reference
Proc. R. Soc. A 8 March 2014 vol. 470 no. 2163, 20130691.
J. Ciambella, G. Saccomandi.
Advanced Composites Centre for Innovation and Science, University of Bristol, Bristol BS8 1TR, UK and
Dipartimento di Ingegneria Strutturale e Geotecnica, Sapienza Università di Roma, Rome 00184, Italy and
Dipartimento di Ingegneria Industriale, Università degli Studi di Perugia,Perugia 06125, Italy.
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 non-monotonic 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.
