Variational formulation on effective elastic moduli of randomly cracked solids

Xu, XF; Stefanou, G

dc.contributor.author	Xu, XF	en
dc.contributor.author	Stefanou, G	en
dc.date.accessioned	2014-03-01T01:37:31Z
dc.date.available	2014-03-01T01:37:31Z
dc.date.issued	2011	en
dc.identifier.issn	1543-1649	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/21542
dc.subject	Green-function-based multiscale method	en
dc.subject	Morphological crack model	en
dc.subject	Randomly cracked solids	en
dc.subject	Variational bounds	en
dc.subject.classification	Engineering, Multidisciplinary	en
dc.subject.classification	Mathematics, Interdisciplinary Applications	en
dc.subject.other	Approximation methods	en
dc.subject.other	Cracked media	en
dc.subject.other	Cracked solid	en
dc.subject.other	Effective elastic modulus	en
dc.subject.other	Hashin-shtrikman	en
dc.subject.other	Inhomogeneous media	en
dc.subject.other	Mechanics models	en
dc.subject.other	Morphological crack model	en
dc.subject.other	Morphological model	en
dc.subject.other	Multiscale method	en
dc.subject.other	Random orientations	en
dc.subject.other	Variational bounds	en
dc.subject.other	Variational formulation	en
dc.subject.other	Variational principles	en
dc.subject.other	Approximation theory	en
dc.subject.other	Cracks	en
dc.subject.other	Elastic moduli	en
dc.subject.other	Mechanics	en
dc.subject.other	Morphology	en
dc.subject.other	Stochastic models	en
dc.subject.other	Variational techniques	en
dc.subject.other	Stress corrosion cracking	en
dc.title	Variational formulation on effective elastic moduli of randomly cracked solids	en
heal.type	journalArticle	en
heal.identifier.primary	10.1615/IntJMultCompEng.v9.i3.60	en
heal.identifier.secondary	http://dx.doi.org/10.1615/IntJMultCompEng.v9.i3.60	en
heal.language	English	en
heal.publicationDate	2011	en
heal.abstract	Formulation of variational bounds for properties of inhomogeneous media constitutes one of the most fundamental parts of theoretical and applied mechanics. The merit of rigorously derived bounds lies in them not only providing verification for approximation methods, but more importantly, serving as the foundation for building up mechanics models. A direct application of classical micromechanics theories to random cracked media, however, faces a problem of singularity due to a zero volume fraction of cracks. In this study a morphological model of random cracks is first established. Based on the morphological model, a variational formulation of randomly cracked solids is developed by applying the stochastic Hashin-Shtrikman variational principle formulated by Xu (J. Eng. Mech., vol. 135, pp. 1180- 1188, 2009) and the Green-function-based method by Xu et al. (Comput. Struct., vol. 87, pp. 1416-1426, 2009). The upper-bound expressions are explicitly given for penny-shaped and slit-like random cracks with parallel and random orientations. Unlike previous works, no special underlying morphology is assumed in the variational formulation, and the bounds obtained are applicable to many realistic non-self-similar morphologies. © 2011 by Begell House, Inc.	en
heal.publisher	BEGELL HOUSE INC	en
heal.journalName	International Journal for Multiscale Computational Engineering	en
dc.identifier.doi	10.1615/IntJMultCompEng.v9.i3.60	en
dc.identifier.isi	ISI:000296217900006	en
dc.identifier.volume	9	en
dc.identifier.issue	3	en
dc.identifier.spage	347	en
dc.identifier.epage	363	en