Micropolar theory for two-dimensional stresses in elastic honeycomb

A micropolar theory has been used to calculate the stress field generated b y a fundamental boundary-value problem in planar elasticity namely, a norma l line force acting on the surface of a honeycomb half-space. In this two-d imensional analysis the microstructure of the honeycomb results in couple s tresses and microrotations in addition to the usual components of stress an d strain. Constitutive relations for a unit cell of the honeycomb are obtai ned that are sensitive to the symmetry of the microstructure. Because of th e six-fold symmetry of the regular hexagonal microstructure, these constitu tive relations contain only four independent material constants. The discon tinuous traction on the boundary of the honeycomb generates stresses sigma( ij) that have a 1/r dependence on radial distance from the discontinuity wh ile the microcouples m(i3) have a 1/r(2) dependence on radial distance.