1 Department of Civil Engineering, The Faculty of Engineering and Science, Aalborg University, VBN2 Dept. of Mechanical Engineering, University of New Mexico3 The Faculty of Engineering and Science, Aalborg University, VBN
We obtain a general solution to the field equations of plane micropolar elasticity for materials characterized by a hexagonal or equilateral triangular structure. These materials exhibit 3-fold symmetry in the plane and the elastic response is isotropic. Utilizing two displacement potential functions, the solution is obtained in terms of two analytic functions and a third function satisfying the modified homogeneous Helmholtz equation. Expressions for the two-dimensional components of displacement, stress, and couple stress, along with the resultant force on a contour, are presented.We observe that micropolar effects are most significant in material regions subjected to large deformation gradients. Specific results are presented for the classical crack problem, the half plane loaded uniformly on the surface, Flamant's problem, and the circular cylinder compressed by equal and opposite oncentrated forces.
European Journal of Mechanics a - Solids, 2008, Vol 27, Issue 1, p. 18-27