Mixed finite element formulation for the general anti-plane shear problem, including mode III crack computations, in the framework of dipolar linear gradient elasticity

Markolefas, SI; Tsouvalas, DA; Tsamasphyros, GI

dc.contributor.author	Markolefas, SI	en
dc.contributor.author	Tsouvalas, DA	en
dc.contributor.author	Tsamasphyros, GI	en
dc.date.accessioned	2014-03-01T01:31:06Z
dc.date.available	2014-03-01T01:31:06Z
dc.date.issued	2009	en
dc.identifier.issn	0178-7675	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19747
dc.subject	Dipolar strain gradient elasticity	en
dc.subject	Mixed finite elements	en
dc.subject	Mixed formulations	en
dc.subject	P-Version	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.classification	Mechanics	en
dc.subject.other	Approximation theory	en
dc.subject.other	Crack tips	en
dc.subject.other	Cracks	en
dc.subject.other	Elasticity	en
dc.subject.other	Finite element method	en
dc.subject.other	Programming theory	en
dc.subject.other	Strain measurement	en
dc.subject.other	Anti planes	en
dc.subject.other	Approximation methods	en
dc.subject.other	Basis functions	en
dc.subject.other	Crack problems	en
dc.subject.other	Crack-tip	en
dc.subject.other	Different length scale	en
dc.subject.other	Dipolar strain gradient elasticity	en
dc.subject.other	Displacement fields	en
dc.subject.other	Exact solutions	en
dc.subject.other	Finite element approximations	en
dc.subject.other	Gradient elasticities	en
dc.subject.other	High orders	en
dc.subject.other	Linear gradients	en
dc.subject.other	Material micro structures	en
dc.subject.other	Mesh refinements	en
dc.subject.other	Micro-scale	en
dc.subject.other	Mixed finite element formulations	en
dc.subject.other	Mixed finite elements	en
dc.subject.other	Mixed formulations	en
dc.subject.other	P versions	en
dc.subject.other	P-Version	en
dc.subject.other	Stress components	en
dc.subject.other	Elastohydrodynamics	en
dc.title	Mixed finite element formulation for the general anti-plane shear problem, including mode III crack computations, in the framework of dipolar linear gradient elasticity	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s00466-008-0340-9	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s00466-008-0340-9	en
heal.language	English	en
heal.publicationDate	2009	en
heal.abstract	A mixed formulation is developed and numerically validated for the general 2D anti-plane shear problem in micro-structured solids governed by dipolar strain gradient elasticity. The current mixed formulation employs the form II statement of the gradient elasticity theory and uses the double stress components and the displacement field as main variables. High order, C 0-continuous, conforming basis functions are employed in the finite element approximations (p-version). The results for the mode III crack problem reveal that, with proper mesh refinement at the areas of high solution gradients, the current approximation method captures the exact solution behaviour at different length scales, which depend on the size of material micro-structure. The latter is of vital importance because, near the crack tip, the nature of the exact solution, changes radically as we proceed from the macro- to micro-scale. © 2008 Springer-Verlag.	en
heal.publisher	SPRINGER	en
heal.journalName	Computational Mechanics	en
dc.identifier.doi	10.1007/s00466-008-0340-9	en
dc.identifier.isi	ISI:000263360500001	en
dc.identifier.volume	43	en
dc.identifier.issue	6	en
dc.identifier.spage	715	en
dc.identifier.epage	730	en