On the coupling number and characteristic length of micropolar media of differing topology

Abstract

In planar micropolar elasticity theory, the degree of micropolarity exhibited by a loaded heterogeneous material is quantified by a dimensionless constitutive parameter, the coupling number. Theoretical predictions of this parameter derived by considering the mechanical behaviour of regular, two-dimensional lattices with straight connectors suggest that its value is dependent on the connectivity or topology of the lattice with the coupling number in a square lattice predicted to be notably higher than in its hexagonal counterpart. A second constitutive parameter reflecting the intrinsic lattice size scale, the characteristic length, is also predicted to be topology-dependent. In this paper, we compare the behaviour of alternative two-dimensional heterogeneous materials in the context of micropolar elasticity. These materials consist of periodic arrays of circular voids within a polymeric matrix rather than a lattice of straight connectors. Two material variants that differ only in their matrix topology are investigated in particular. Values of the additional micropolar constitutive parameters are obtained for each material from both experimental tests and finite-element analyses. The values determined for these parameters, particularly the coupling number, suggest that their topological dependence differs appreciably from the theoretical predictions of the lattice models.