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

M. McGregor, M. A. Wheel

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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 noticeably 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.
Original languageEnglish
Article number20140150
Number of pages19
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Early online date17 Jun 2014
Publication statusPublished - 16 Jul 2014


  • micropolar elasticity
  • Cosserat elasticity
  • size effect
  • constitutive properties
  • characteristic length
  • coupling number


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