A new microstructure-dependent Saint-Venant torsion model based on a modified couple stress theory

Tsiatas, GC; Katsikadelis, JT

dc.contributor.author	Tsiatas, GC	en
dc.contributor.author	Katsikadelis, JT	en
dc.date.accessioned	2014-03-01T01:34:55Z
dc.date.available	2014-03-01T01:34:55Z
dc.date.issued	2011	en
dc.identifier.issn	0997-7538	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20938
dc.subject	Analog equation method	en
dc.subject	Couple stress theory	en
dc.subject	Method of fundamental solutions	en
dc.subject	Microstructure	en
dc.subject	Strain gradient elasticity	en
dc.subject	Torsion	en
dc.subject.classification	Mechanics	en
dc.subject.other	Analog equation methods	en
dc.subject.other	Arbitrary cross section	en
dc.subject.other	Couple stress	en
dc.subject.other	Couple stress theory	en
dc.subject.other	Current models	en
dc.subject.other	Deformable bodies	en
dc.subject.other	Developed model	en
dc.subject.other	Direct Boundary Element Method	en
dc.subject.other	Fourth order partial differential equations	en
dc.subject.other	Fundamental solutions	en
dc.subject.other	Governing differential equations	en
dc.subject.other	Gradient elasticity	en
dc.subject.other	Kirchhoff plates	en
dc.subject.other	Material length scale	en
dc.subject.other	Method of fundamental solutions	en
dc.subject.other	Micron scale	en
dc.subject.other	Model-based OPC	en
dc.subject.other	Neumann boundary condition	en
dc.subject.other	Saint-Venant torsion	en
dc.subject.other	Strain gradient elasticity	en
dc.subject.other	Tensile membrane	en
dc.subject.other	Torsional response	en
dc.subject.other	Warping function	en
dc.subject.other	Boundary conditions	en
dc.subject.other	Elasticity	en
dc.subject.other	Elastohydrodynamics	en
dc.subject.other	Microstructure	en
dc.subject.other	Partial differential equations	en
dc.subject.other	Torsional stress	en
dc.subject.other	Boundary element method	en
dc.title	A new microstructure-dependent Saint-Venant torsion model based on a modified couple stress theory	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/j.euromechsol.2011.03.007	en
heal.identifier.secondary	http://dx.doi.org/10.1016/j.euromechsol.2011.03.007	en
heal.language	English	en
heal.publicationDate	2011	en
heal.abstract	In this paper a new modified couple stress model is developed for the Saint-Venant torsion problem of micro-bars of arbitrary cross-section. The proposed model is derived from a modified couple stress theory and has only one material length scale parameter. Using a variational procedure the governing differential equation and the associated boundary conditions are derived in terms of the warping function. This is a fourth order partial differential equation representing the analog of a Kirchhoff plate having the shape of the cross-section and subjected to a uniform tensile membrane force with mixed Neumann boundary conditions. Since the fundamental solution of the equation is known, the problem could be solved using the direct Boundary Element Method (BEM). In this investigation, however, the Analog Equation Method (AEM) solution is applied and the results are cross checked using the Method of Fundamental Solutions (MFS). Several micro-bars of various cross-sections are analyzed to illustrate the applicability of the developed model and to reveal the differences between the current model and an existing one which, however, contains two additional constants related to the microstructure. Moreover, useful conclusions are drawn from the micron-scale torsional response of micro-bars, giving thus a better insight in the gradient elasticity approach of the deformable bodies. (C) 2011 Elsevier Masson SAS. All rights reserved.	en
heal.publisher	GAUTHIER-VILLARS/EDITIONS ELSEVIER	en
heal.journalName	European Journal of Mechanics, A/Solids	en
dc.identifier.doi	10.1016/j.euromechsol.2011.03.007	en
dc.identifier.isi	ISI:000293485200012	en
dc.identifier.volume	30	en
dc.identifier.issue	5	en
dc.identifier.spage	741	en
dc.identifier.epage	747	en