Strain gradient theory with couple stress for crystalline solids

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	Strain gradient theory with couple stress for crystalline solids
	Chen SH(陈少华); Wang ZQ(王自强)
刊名	European Journal of Mechanics A-Solids
	2001
卷号	20 期号:5 页码:739-756
ISSN号	0997-7538
通讯作者	Chen, SH (reprint author), Chinese Acad Sci, Inst Mech, LNM, Beijing 100080, Peoples R China.
中文摘要	A new phenomenological strain gradient theory for crystalline solid is proposed. It fits within the framework of general couple stress theory and involves a single material length scale Ics. In the present theory three rotational degrees of freedom omega (i) are introduced, which denote part of the material angular displacement theta (i) and are induced accompanying the plastic deformation. omega (i) has no direct dependence upon u(i) while theta = (1 /2) curl u. The strain energy density omega is assumed to consist of two parts: one is a function of the strain tensor epsilon (ij) and the curvature tensor chi (ij), where chi (ij) = omega (i,j); the other is a function of the relative rotation tensor alpha (ij). alpha (ij) = e(ijk) (omega (k) - theta (k)) plays the role of elastic rotation reason The anti-symmetric part of Cauchy stress tau (ij) is only the function of alpha (ij) and alpha (ij) has no effect on the symmetric part of Cauchy stress sigma (ij) and the couple stress m(ij). A minimum potential principle is developed for the strain gradient deformation theory. In the limit of vanishing l(cs), it reduces to the conventional counterparts: J(2) deformation theory. Equilibrium equations, constitutive relations and boundary conditions are given in detail. For simplicity, the elastic relation between the anti-symmetric part of Cauchy stress tau (ij), and alpha (ij) is established and only one elastic constant exists between the two tensors. Combining the same hardening law as that used in previously by other groups, the present theory is used to investigate two typical examples, i.e., thin metallic wire torsion and ultra-thin metallic beam bend, the analytical results agree well with the experiment results. While considering the, stretching gradient, a new hardening law is presented and used to analyze the two typical problems. The flow theory version of the present theory is also given.
学科主题	力学
类目[WOS]	Mechanics
研究领域[WOS]	Mechanics
关键词[WOS]	STRUCTURED SOLIDS ; DYNAMICAL THEORY ; PLASTICITY
收录类别	SCI ; EI
语种	英语
WOS记录号	WOS:000171565100004
公开日期	2007-06-15
内容类型	期刊论文
源URL	[http://dspace.imech.ac.cn/handle/311007/16198]
专题	力学研究所_力学所知识产出(1956-2008)
推荐引用方式 GB/T 7714	Chen SH,Wang ZQ. Strain gradient theory with couple stress for crystalline solids[J]. European Journal of Mechanics A-Solids,2001,20(5):739-756.
APA	陈少华,&王自强.(2001).Strain gradient theory with couple stress for crystalline solids.European Journal of Mechanics A-Solids,20(5),739-756.
MLA	陈少华,et al."Strain gradient theory with couple stress for crystalline solids".European Journal of Mechanics A-Solids 20.5(2001):739-756.