Asimmetrical Pseudoelasticity

TL;DR

This paper introduces a new theory of asymmetrical pseudoelasticity linking symmetrical stress and strain tensors via an asymmetrical material tensor, expanding traditional elasticity models and providing generalized solutions.

Contribution

It develops a novel 6-dimensional asymmetrical elasticity matrix with unique invariance properties, extending classical symmetry assumptions in continuum mechanics.

Findings

Constructed an invariable asymmetrical elasticity matrix with eight independent components.

Generalized classical solutions to include new kinematic effects.

Expanded the scope of elasticity theory beyond traditional transversally isotropic materials.

Abstract

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.