Theory of Micropolar Elasticity

Abstract

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On dislocations in a special class of generalized elasticity

“…The higher order stresses τ ijk and λ ijk are called double force stress and double couple stress, respectively. The constitutive relations for isotropic micropolar elasticity (see, e.g., [10,39,40]) have the form…”

“…Using the six material constants of a Cosserat continuum (micropolar medium), two characteristic lengths l and h can be defined by [39,40] 24) which are Cosserat intrinsic lengths. The above equations (3.20) and (3.21) may be expressed in terms of stresses…”

“…The expressions for the force stresses and couple stresses of a screw dislocations in a Cosserat continuum or micropolar medium were given by Kessel [41] (see also [39,40,42,43]). In micropolar elasticity, the asymmetric force stresses of a straight screw dislocation may be given in terms of the stress function…”

“…We use the stress function formulation given by [46,47] (see also [38,40,43]), which involves two stress functions obtain for the modified stress functions the following inhomogeneous Helmholtz equations and Due to the special choice of cylindrical coordinates the couple stresses (3.116)-(3.119) have an artifical discontinuity at r = 0. At r = 0 the radial part of the couple stresses is finite and is multiplied by cos ϕ or sin ϕ.…”

Distributed dislocation approach for cracks in couple-stress elasticity: shear modes

“…Finally, it is worth noting that in the micropolar (Cosserat) theory of elasticity (see e.g. Nowacki, 1972), the traction boundary conditions are six since the rotation is fully independent of the displacement vector. In this case the tractions can directly be derived from the equilibrium of the material tetrahedron, i.e.…”