Deviatoric couple stress theory and its application to simple shear and pure bending problems

doi:10.1016/j.apm.2024.115799

IMECH-IR > 非线性力学国家重点实验室

	Deviatoric couple stress theory and its application to simple shear and pure bending problems
	Wang, YaWei ; Chen J(陈健); Li, XianFang
发表期刊	APPLIED MATHEMATICAL MODELLING
	2025-02
卷号	138 页码:115799
ISSN	0307-904X
摘要	Classical couple stress theory is indeterminate since the number of independent basic equations inconsistent with that of field variables and the corresponding differential equation is not closed. The purpose of this paper is to remedy this gap and it is proven that the spherical part of couple stress tensor vanishes when neglecting torsional deformation. With the vanishing trace the couple stress tensor as a premise, the deviatoric (or traceless) couple stress theory (DCST) is considered. Besides basic equations, the governing equation along with appropriate boundary conditions is given for a three-dimensional problem. Two special cases of plane problems and anti plane problems are also provided. A simple shear problem is considered to show the advantage of the DCST. An elastic layer with a clamped surface under uniform shear loading on the other surface is solved. Exact solution of the in-plane and anti-plane shear problems of an elastic strip is determined and however, the former has no solution if classical elasticity is used. The results indicate that there exists a boundary layer near the clamped surface of the strip or a great stress gradient occurs near the clamped surface when the characteristic length is sufficiently small. annulus subjected to anti-plane shear loading on the inner edge and fixed on the outer edge and the pure bending of a 3D bar with rectangular cross-section are analyzed to illustrate size-dependent effect. Modified couple stress theory and consistent couple stress theory can reduced as two extreme cases of the present theory.
关键词	Couple stress Deviatoric couple stress theory Governing equation Boundary layer Shear problem
DOI	10.1016/j.apm.2024.115799
收录类别	SCI ; EI
语种	英语
WOS记录号	WOS:001358636000001
WOS研究方向	Engineering ; Mathematics ; Mechanics
WOS类目	Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics
项目资助者	National Natural Science Foundation of China {12072374, 12372086]
论文分区	一类
力学所作者排名	2
RpAuthor	Li XF
引用统计
文献类型	期刊论文
条目标识符	http://dspace.imech.ac.cn/handle/311007/97196
专题	非线性力学国家重点实验室
作者单位	1.【Wang, Ya-Wei & Li, Xian-Fang】 Cent South Univ, Sch Civil Engn, Changsha 410075, Peoples R China 2.【Chen, Jian】 Chinese Acad Sci, Inst Mech, State Key Lab Nonlinear Mech, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wang, YaWei,Chen J,Li, XianFang. Deviatoric couple stress theory and its application to simple shear and pure bending problems[J]. APPLIED MATHEMATICAL MODELLING,2025,138:115799.Rp_Au:Li XF
APA	Wang, YaWei,陈健,&Li, XianFang.(2025).Deviatoric couple stress theory and its application to simple shear and pure bending problems.APPLIED MATHEMATICAL MODELLING,138,115799.
MLA	Wang, YaWei,et al."Deviatoric couple stress theory and its application to simple shear and pure bending problems".APPLIED MATHEMATICAL MODELLING 138(2025):115799.