Defining Equations of the Anisotropic Moment Linear Theory of Elasticity and the Two-Dimensional Problem of Pure Shear with Constrained Rotation

Abstract

The paper presents the equations of the linear moment theory of elasticity for the case of arbitrary anisotropy of material tensors of the fourth rank. Symmetric and skew-symmetric components are distinguished in the defining relations. Some simplified versions of linear defining relations are considered. The possibility of Cauchy elasticity is allowed when material tensors of the fourth rank do not have the main symmetry. For material tensors that determine force and couple stresses, we introduce eigenmoduli and eigenstates that are invariant characteristics of an elastic moment medium. For the case of plane deformation and constrained rotation, an example of a complete solution of the two-dimensional problem is given when there are only shear stresses. The solutions turn out to be significantly different for anisotropic and isotropic elastic media.