QQ客服 官方微博 反馈留言

	Strain rates and material spins
	Xiao, H ; Bruhns, OT ; Meyers, ATM
	1998
关键词	strain measures spin tensors material time rate objective corotational rates general explicit expressions LOGARITHMIC STRAIN STRESS RATE DEFORMATION GRADIENT FINITE DEFORMATIONS ISOTROPIC FUNCTIONS COROTATIONAL RATES SOLID MECHANICS STRETCH TENSORS HILLS STRAIN TIME RATES
英文摘要	The material time rate of Lagrangean strain measures, objective corotational rates of Eulerian strain measures and their defining spin tensors are investigated from a general point of view. First, a direct and rigorous method is used to derive a simple formula for the gradient of the tenser-valued function defining a general class of strain measures. By means of this formula and the chain rule as well as Sylvester's formula for eigenprojections, explicit basis-free expressions for the material time rate of an arbitrary Lagrangean strain measure can be derived in terms of the right Cauchy-Green tensor and the material time rate of any chosen Lagrangean strain measure, e.g. Hencky's logarithmic strain measure. These results provide a new derivation of Carlson-Hoger's general gradient formula for an arbitrary generalized strain measure and supply a new, rigorous proof for Carlson-Hoger's conjecture concerning the n-dimensional case. Next, by virtue of the aforementioned gradient formula, a general fact for objective corotational rates and their defining spin tensors is disclosed: Let Omega = Y (B, D, W) be any spin tensor that is continuous with respect to B, where B, D and W are the left Cauchy-Green tensor, the stretching tensor and the vorticity tensor. Then the corotational rate of an Eulerian strain measure defined by B is objective if and only if Omega = W + (Y) over tilde(B, D), where (Y) over tilde is isotropic. By means of this fact and certain necessary or reasonable requirements, it is further 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. A general basis-free expression for all such spin tensors and accordingly a general basis-free expression for a general class of objective corotational rates of an arbitrary Eulerian strain measure are established in terms of the left Cauchy-Green tensor B and the stretching tensor D as well as the introduced antisymmetric function. By choosing several particular forms of the latter, all commonly-known spin tensors and corresponding corotational rates are shown to be incorporated into these general formulas in a natural way. In particular, with the aid of these general formulae it is proved that an objective corotational rate of the Eulerian logarithmic strain measure In V is identical with the stretching tensor D and moreover that in all possible strain tensor measures only In V enjoys this property.; Engineering, Multidisciplinary; Materials Science, Multidisciplinary; Mechanics; SCI(E); 93; ARTICLE; 1; 1-41; 52
语种	英语
出处	SCI
出版者	弹性学杂志
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/217881]
专题	数学科学学院
推荐引用方式 GB/T 7714	Xiao, H,Bruhns, OT,Meyers, ATM. Strain rates and material spins. 1998-01-01.

个性服务

查看访问统计

相关权益政策

暂无数据

收藏/分享

除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。