A Quest for Micropolar Elastic Constants

Abstract

In contrast to a homogeneous isotropic elastic medium with only two elastic constants, a linear elastic micropolar solid is characterized by six such constants. To evaluate these constants it is necessary to solve selected boundary-value problems in terms of measurable surface tractions and displacements. Representative problems are tension and torsion of a circular cylinder and cylindrical bending of a rectangular plate. Analytical solutions to these static problems have been obtained, and to complement these solutions a combination of experiments was planned and a novel man-made micropolar solid was developed. The solid consisted of a composite material with aluminum shot uniformly distributed throughout an epoxy matrix. The shot, with an elastic modulus 20 times that of the matrix, was selected to represent rigid microelements embedded in a deformable medium and thereby model a micropolar solid. Static torsion tests revealed that the micropolar effects were masked by material inhomogeneity. It was concluded that, to within the resolution of the measurements, the special material developed here behaved as a classical elastic solid. Detection of possible micropolar phenomena will demand either higher resolution static measurements or a series of dynamic tests.