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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Defining Equations of the Anisotropic Moment Linear Theory of Elasticity and the Two-Dimensional Problem of Pure Shear with Constrained Rotation. / Annin, B. D.; Ostrosablin, N. I.; Ugryumov, R. I.

In: Journal of Applied and Industrial Mathematics, Vol. 17, No. 1, 03.2023, p. 1-14.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{399ce20b191749fe92752847fd34f645,

title = "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 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.",

keywords = "asymmetric stress tensor, constrained rotation, defining equation, elastic modulus, fourth-rank tensor, moment theory of elasticity, pure shear, two-dimensional problem",

author = "Annin, {B. D.} and Ostrosablin, {N. I.} and Ugryumov, {R. I.}",

note = "The work was carried out within the framework of the Program of Fundamental Research of the Siberian Branch of the Russian Academy of Sciences, project no. 2.3.1.3.1. Публикация для корректировки.",

year = "2023",

month = mar,

doi = "10.1134/S1990478923010015",

language = "English",

volume = "17",

pages = "1--14",

journal = "Journal of Applied and Industrial Mathematics",

issn = "1990-4789",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "1",

}

RIS

TY - JOUR

T1 - Defining Equations of the Anisotropic Moment Linear Theory of Elasticity and the Two-Dimensional Problem of Pure Shear with Constrained Rotation

AU - Annin, B. D.

AU - Ostrosablin, N. I.

AU - Ugryumov, R. I.

N1 - The work was carried out within the framework of the Program of Fundamental Research of the Siberian Branch of the Russian Academy of Sciences, project no. 2.3.1.3.1. Публикация для корректировки.

PY - 2023/3

Y1 - 2023/3

N2 - 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.

AB - 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.

KW - asymmetric stress tensor

KW - constrained rotation

KW - defining equation

KW - elastic modulus

KW - fourth-rank tensor

KW - moment theory of elasticity

KW - pure shear

KW - two-dimensional problem

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85159315747&origin=inward&txGid=7e5b9b854cf192ee5e65916e042fa793

UR - https://www.mendeley.com/catalogue/d9cb29e9-f856-334d-8bd8-149ed69a0760/

U2 - 10.1134/S1990478923010015

DO - 10.1134/S1990478923010015

M3 - Article

VL - 17

SP - 1

EP - 14

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 1

ER -

ID: 59244740