  Term "asymmetrical pseudoelasticity" refers to the theory, in which a
symmetrical stress tensor and a symmetrical strain tensor are connected by
means of an asymmetrical material tensor. An 6-dimensional asymmetrical matrix
of elasticity has been constructed that is invariable in relation to orthogonal
transformation with a single rotation operator and coordinated with
conservation laws of the continuum mechanics. The matrix has got eight
independent components and expands the traditional definition of transversally
isotropic (hexagonal) material symmetry. The suggested theory includes
definition of 3-dimensional and 2-dimensional linear boundary value problems
and accurate solutions generalizing the traditional polynomial solutions, A.
Love's solutions, and N.I. Muskhelishvili's solutions and providing new
kinematic effects.
