A continuum approach for the large strain finite element analysis of auxetic materials

Auxetic materials are materials which present negative Poisson ratios. This unusual behavior is due to their particular microstructures. It is frequent that during large deformation processes in auxetic foams, the value of the Poisson ratio also presents large variations, with transitions from auxetic to conventional behavior. In this paper we present a procedure to perform large strain finite element analysis of energy-conservative isotropic auxetic materials from a continuum perspective. Two possible approaches are used. The first one is based on uncoupled WYPiWYG hyperelasticity. This decomposition permits a simple analysis of the behavior using also infinitesimal bi-linear models. The second approach is a novel procedure for coupled hyperelasticity based on classical invariants. This latter procedure is amenable for obtaining the stored energy of highly compressible foams, including coupling terms and generic invariants, as for example those used by the analytical Blatz-Ko model or the hyperelastic model of Ciambella and Saccomandi, which was explicitly developed for auxetic foams. The applicability and efficiency of the method is shown through fmite element analyses of auxetic foams at large strains using the continuum approach. (C) 2017 Elsevier Ltd. All rights reserved.