Numerical solution of crack problems in gradient elasticity

Papanicolopulos, S-A; Zervos, A

dc.contributor.author	Papanicolopulos, S-A	en
dc.contributor.author	Zervos, A	en
dc.date.accessioned	2014-03-01T01:59:47Z
dc.date.available	2014-03-01T01:59:47Z
dc.date.issued	2010	en
dc.identifier.issn	17550777	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/29044
dc.subject	Mathematical modelling	en
dc.subject	Strength & testing of materials	en
dc.subject	Stress analysis	en
dc.subject.other	Crack problems	en
dc.subject.other	Discretisation	en
dc.subject.other	Displacement formulation	en
dc.subject.other	Elastic materials	en
dc.subject.other	Finite-element	en
dc.subject.other	Gradient elasticity	en
dc.subject.other	Higher order terms	en
dc.subject.other	Mathematical modelling	en
dc.subject.other	Numerical results	en
dc.subject.other	Numerical scheme	en
dc.subject.other	Numerical solution	en
dc.subject.other	Second order derivatives	en
dc.subject.other	Stress and strain	en
dc.subject.other	Three-dimensional elements	en
dc.subject.other	Cracks	en
dc.subject.other	Elastohydrodynamics	en
dc.subject.other	Fracture mechanics	en
dc.subject.other	Materials testing	en
dc.subject.other	Mathematical models	en
dc.subject.other	Microstructure	en
dc.subject.other	Numerical analysis	en
dc.subject.other	Strain	en
dc.subject.other	Stress analysis	en
dc.subject.other	Elasticity	en
dc.title	Numerical solution of crack problems in gradient elasticity	en
heal.type	journalArticle	en
heal.identifier.primary	10.1680/eacm.2010.163.2.73	en
heal.identifier.secondary	http://dx.doi.org/10.1680/eacm.2010.163.2.73	en
heal.publicationDate	2010	en
heal.abstract	Gradient elasticity is a constitutive framework that takes into account the microstructure of an elastic material. It considers that, in addition to the strains, second-order derivatives of the displacement also affect the energy stored in the medium. Three different yet equivalent forms of gradient elasticity can be found in the literature, reflecting the different ways in which the second-order derivatives can be grouped to form other physically meaningful quantities. This paper presents a general discretisation of gradient elasticity that can be applied to all three forms, based on the finite-element displacement formulation. The presence of higher order terms requires C1-continuous interpolation, and some appropriate two- and three-dimensional elements are presented. Numerical results for the displacement, stress and strain fields around cracks are shown and compared with available solutions, demonstrating the robustness and accuracy of the numerical scheme and investigating the effect of microstructure in the context of fracture mechanics.	en
heal.journalName	Proceedings of the Institution of Civil Engineers: Engineering and Computational Mechanics	en
dc.identifier.doi	10.1680/eacm.2010.163.2.73	en
dc.identifier.volume	163	en
dc.identifier.issue	2	en
dc.identifier.spage	73	en
dc.identifier.epage	82	en