| Deviatoric couple stress theory and its application to simple shear and pure bending problems | |
| Wang, YaWei; Chen J(陈健); Li, XianFang | |
| Source Publication | APPLIED MATHEMATICAL MODELLING
 |
| 2025-02 | |
| Volume | 138Pages:115799 |
| ISSN | 0307-904X |
| Abstract | 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. |
| Keyword | Couple stress Deviatoric couple stress theory Governing equation Boundary layer Shear problem |
| DOI | 10.1016/j.apm.2024.115799 |
| Indexed By | SCI ; EI |
| Language | 英语 |
| WOS ID | WOS:001358636000001 |
| WOS Research Area | Engineering ; Mathematics ; Mechanics |
| WOS Subject | Engineering, Multidisciplinary ; Mathematics, Interdisciplinary Applications ; Mechanics |
| Funding Organization | National Natural Science Foundation of China {12072374, 12372086] |
| Classification | 一类 |
| Ranking | 2 |
| Contributor | Li XF |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://dspace.imech.ac.cn/handle/311007/97196 |
| Collection | 非线性力学国家重点实验室 |
| Affiliation | 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 |
| Recommended Citation 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. |
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