Eringen's model via linearization of nonlocal hyperelasticity

被引：2

作者：

Bellido, Jose C. ^{[1
,2
,6
,7
]}

Cueto, Javier ^{[3
]}

Mora-Corral, Carlos ^{[4
,5
]}

机构：

[1] Univ Castilla La Mancha, ETSI Ind, Ciudad Real, Spain

[2] Univ Castilla La Mancha, Dept Math, Ciudad Real, Spain

[3] Univ Nebraska Lincoln, Dept Math, Lincoln, NE USA

[4] Univ Autonoma Madrid, Dept Matemat, Madrid, Spain

[5] UAM, Inst Ciencias Matemat, CSIC, UC3M & UCM, Madrid, Spain

[6] Univ Castilla La Mancha, ETSI Ind, Ciudad Real 13071, Spain

[7] Univ Castilla La Mancha, Dept Math, Ciudad Real 13071, Spain

来源：

MATHEMATICS AND MECHANICS OF SOLIDS | 2024年 / 29卷 / 04期

关键词：

Nonlocal elasticity; Riesz fractional and nonlocal gradients; linearization of nonlocal equations; Eringen model of elasticity; nonlocal Korn's inequality; ELASTICITY; EXISTENCE;

D O I：

10.1177/10812865231208437

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

We consider Riesz' fractional gradient and a truncated version of it. The equations of nonlocal nonlinear elasticity based on those gradients are known. We perform a formal linearization and arrive at the equations of linear elasticity based on those nonlocal operators. We prove the existence of solutions of the linear equations, notably, by a nonlocal version of Korn's inequality. Finally, we show that the linearizations obtained are particular cases of Eringen's model with singular kernels.

引用

页码：686 / 703

页数：18

共 31 条

[1]

ACOSTA G., 2017, Divergence Operator and Related Inequalities

[2]

Adams R.A., 1975, Pure Appl. Math

[3]

BALL JM, 1977, ARCH RATION MECH AN, V63, P337, DOI 10.1007/BF00279992

[4] Minimizers of nonlocal polyconvex energies in nonlocal hyperelasticity [J].