Elasto-static micropolar behavior of a chiral auxetic lattice

Auxetic materials expand when stretched, and shrink when compressed. This is the result of a negative Poisson's ratio νν. Isotropic configurations with ν≈−1ν≈−1 have been designed and are expected to provide increased shear stiffness G  . This assumes that Young's modulus and νν can be engineered independently. In this article, a micropolar-continuum model is employed to describe the behavior of a representative auxetic structural network, the chiral lattice, in an attempt to remove the indeterminacy in its constitutive law resulting from ν=−1ν=−1. While this indeterminacy is successfully removed, it is found that the shear modulus is an independent parameter and, for certain configurations, it is equal to that of the triangular lattice. This is remarkable as the chiral lattice is subject to bending deformation of its internal members, and thus is more compliant than the triangular lattice which is stretch dominated. The derived micropolar model also indicates that this unique lattice has the highest characteristic length scale lc of all known lattice topologies, as well as a negative first Lamé constant without violating bounds required for thermodynamic stability. We also find that hexagonal arrangements of deformable rings have a coupling number N=1. This is the first lattice reported in the literature for which couple-stress or Mindlin theory is necessary rather than being adopted a priori.

► The 2D auxetic materials have shear modulus bound by that of microstructures with axial deformations.
► Micropolar model is a continuous function of topology ranging from chiral to triangular lattices.
► Poisson's ratio shows boundary-layer behavior going from chiral to triangular configurations.
► The chiral lattice has highest characteristic length of all lattices reported in the literature.
► Hexagonal arrangements of deformable rings have coupling number N=1 requiring Mindlin theory.