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

Defining Equations of the Anisotropic Moment Linear Theory of Elasticity and the Two-Dimensional... The paper presents the equations of the linear moment theory of elasticity for the case ofarbitrary anisotropy of material tensors of the fourth rank. Symmetric and skew-symmetriccomponents are distinguished in the defining relations. Some simplified versions of linear definingrelations are considered. The possibility of Cauchy elasticity is allowed when material tensors ofthe fourth rank do not have the main symmetry. For material tensors that determine force andcouple stresses, we introduce eigenmoduli and eigenstates that are invariant characteristics of anelastic moment medium. For the case of plane deformation and constrained rotation, an exampleof 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Applied and Industrial Mathematics Springer Journals

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

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References (18)

Publisher
Springer Journals
Copyright
Copyright © Pleiades Publishing, Ltd. 2023
ISSN
1990-4789
eISSN
1990-4797
DOI
10.1134/s1990478923010015
Publisher site
See Article on Publisher Site

Abstract

The paper presents the equations of the linear moment theory of elasticity for the case ofarbitrary anisotropy of material tensors of the fourth rank. Symmetric and skew-symmetriccomponents are distinguished in the defining relations. Some simplified versions of linear definingrelations are considered. The possibility of Cauchy elasticity is allowed when material tensors ofthe fourth rank do not have the main symmetry. For material tensors that determine force andcouple stresses, we introduce eigenmoduli and eigenstates that are invariant characteristics of anelastic moment medium. For the case of plane deformation and constrained rotation, an exampleof 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.

Journal

Journal of Applied and Industrial Mathematics – Springer Journals

Published: Mar 1, 2023

Keywords: moment theory of elasticity; asymmetric stress tensor; defining equation; elastic modulus; fourth-rank tensor; pure shear; constrained rotation; two-dimensional problem

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