Heuristic molecular modelling of quasi-isotropic auxetic metamaterials under large deformations

A two-dimensional molecular model is presented for the elastic non-linear modelling and design of meta-materials. The fundamental unit-cell, based on a heuristic molecule (HM) approach, is composed of atoms that interact through centred and non-centred spring-based bonds. The kinematics formulation allows to consider large displacements and finite strains while the specific topology of the HM can be parametrized to modify the shape of the rigid atoms and the size of the bonds. The HM is frame indifferent and provides a remarkable quasi-isotropic elastic response for both deviatoric and volumetric large deformation modes. At a macro-scale, the relationship with different continuum materials is given through a standard isotropic Cauchy up to an isotropic Cosserat solid. Evidence on the interest of the model as a calculation tool is provided by studying the elastic response of standard and auxetic materials subjected to a non-homogeneous deformation field, as well as the response of auxetic foams under large deformations. Aside the numerical agreement, it is highlighted how the tailoring of the HM topology can be effective to approximate the non-linear geometric effects that occur at finer scales of auxetic foams. In perspective, we address how the exotic mechanical properties provided by the HM, together with the assumed physical-driven framework, can foster the engineering application and the design of new meta-materials.