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	On objective corotational rates and their defining spin tensors
	Xiao, H ; Bruhns, OT ; Meyers, A
	1998
关键词	FINITE DEFORMATIONS ISOTROPIC FUNCTIONS LOGARITHMIC STRAIN STRETCH STRESS REPRESENTATION MECHANICS ROTATION CONTINUA
英文摘要	In this paper, we prove a general result on objective corotational rates and their defining spin tensors: let Omega* be a spin tensor that is associated with the rotation and deformation of a deforming material body in an arbitrary manner indicated by Omega* = Y(B, D, W), where B and D and W are the left Cauchy-Green tensor and the stretching tensor and the vorticity tensor, respectively. Then the corotational rate of sigma defined by the spin Omega*, i.e., the tensor field <(sigma)over circle>* = <(sigma)over dot> + sigma Omega* - Omega*sigma, is objective for every time-differentiable objective Eulerian symmetric tensor field sigma if and only if the spin tensor Omega* assumes the form Omega* = W + (Y) over tilde(B, D), where (Y) over tilde(B, D) is an antisymmetric tenser-valued isotropic Function. Furthermore, by virtue of certain necessary or reasonable requirements, it is found that a single antisymmetric function of two positive real variables can be introduced to characterize a general class of spin tensors defining objective corotational rates. Accordingly, a general explicit basis-free expression for the latter is established in terms of the left Cauchy-Green tensor B, the vorticity tensor W and the stretching tensor D as well as the introduced antisymmetric function. By choosing several particular forms of the latter, it is shown that all commonly-used spin tensors are incorporated into this general expression in a natural way. (C) 1998 Elsevier Science Ltd. All rights reserved.; Mechanics; SCI(E); 50; ARTICLE; 30; 4001-4014; 35
语种	英语
出处	SCI
出版者	international journal of solids and structures
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/215728]
专题	数学科学学院
推荐引用方式 GB/T 7714	Xiao, H,Bruhns, OT,Meyers, A. On objective corotational rates and their defining spin tensors. 1998-01-01.

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