STRESS INVARIANCE IN PLANAR COSSERAT ELASTICITY

We extend the CLM theorem (Cherkaev, Lurie & Milton, Proc. R. Soc. Lon d. A (1992) 438, 519-529) to planar linear elastic materials of Cosser at (micropolar) type, that is those having microrotation as an additio nal degree of freedom besides the two in-plane displacements. More spe cifically, it is shown that in the first planar problem of such media with smoothly varying material properties, a shift in three, out of fo ur, compliances is possible without changing the stress field; the fou rth coefficient represents a connection between the couple stress tens or and the torsion tensor, while the other three represent compliances relating traction-stress vector with the strains. Same shift holds fo r a locally anisotropic material, whereby the shift tensor is seen to be a multiple of a rotation by a right angle; a null-Lagrangian formul ation is set up on this basis. These results are obtained for material s with smooth properties, with natural implications being drawn for th eir macroscopically effective moduli. Also, it is shown that no shift is possible in case of a pseudo-continuum - a material admitting coupl e stresses but restricted to have the same connection between rotation and displacement gradient as in classical elasticity. Finally, we est ablish that there is no shift in the second planar problem which repre sents a micropolar generalization of the classical out-of-plane elasti city.