Orientation distribution function in non-affine rotations

Dafalias, YF

dc.contributor.author	Dafalias, YF	en
dc.date.accessioned	2014-03-01T01:16:55Z
dc.date.available	2014-03-01T01:16:55Z
dc.date.issued	2001	en
dc.identifier.issn	0022-5096	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14268
dc.subject	A. Microstructures	en
dc.subject	A. Voids and inclusions	en
dc.subject	B. Anisotropic material	en
dc.subject	C. Constitutive behavior	en
dc.subject	Orientation distribution function	en
dc.subject.classification	Materials Science, Multidisciplinary	en
dc.subject.classification	Mechanics	en
dc.subject.classification	Physics, Condensed Matter	en
dc.subject.other	Anisotropy	en
dc.subject.other	Crystal microstructure	en
dc.subject.other	Deformation	en
dc.subject.other	Gradient methods	en
dc.subject.other	Orientation distribution functions (ODF)	en
dc.subject.other	Crystal orientation	en
dc.title	Orientation distribution function in non-affine rotations	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0022-5096(01)00065-5	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0022-5096(01)00065-5	en
heal.language	English	en
heal.publicationDate	2001	en
heal.abstract	The orientation distribution function (ODF) for a class of directional elements, represented by unit vectors or orthonormal triads, which are embedded in a deforming continuum, is obtained by a novel approach in closed analytical form as a function of appropriate deformation and rotation measures, for orientational processes which can be characterized as non-affine rotations. The main conceptual innovation is the introduction of a fictitious motion defined locally in the neighborhood of a material point, such that a directional element which follows non-affine rotation in relation to the real motion, follows affine rotation in relation to the fictitious motion. A key point of the analysis is the time integration of the velocity gradient of the fictitious motion under steady-state conditions for the real velocity gradient, in order to obtain the corresponding local fictitious deformation gradient, from which the ODF for non-affine rotations is calculated by standard methods applicable to affine rotations. Many examples illustrate the foregoing theoretical findings. The ODFs associated with sequences of different deformation processes, which were too difficult to yield a solution in the past, are now readily obtained by the above approach for both affine and non-affine rotations, while previously reported results are retrieved as particular cases with a modicum of analytical calculations. (C) 2001 Elsevier Science Ltd. All rights reserved.	en
heal.publisher	PERGAMON-ELSEVIER SCIENCE LTD	en
heal.journalName	Journal of the Mechanics and Physics of Solids	en
dc.identifier.doi	10.1016/S0022-5096(01)00065-5	en
dc.identifier.isi	ISI:000171975600004	en
dc.identifier.volume	49	en
dc.identifier.issue	11	en
dc.identifier.spage	2493	en
dc.identifier.epage	2516	en