Accuracy of the replacement relations for materials with non-ellipsoidal inhomogeneities. (1st January 2017)

• Record Type: Journal Article
• Authors: Chen, Fengjuan; Sevostianov, Igor; Giraud, Albert; Grgic, Dragan
• Is Part Of: International journal of solids and structures. Volume 104/105(2016)
• Page Start: 73
• Page End: 80
• Publication Date: 2017-01-01
• Subjects: Replacement relation -- Effective properties -- Supersphere; Mechanics, Applied -- Periodicals; Structural analysis (Engineering) -- Periodicals; Elastic solids -- Periodicals; Mécanique appliquée -- Périodiques; Constructions, Théorie des -- Périodiques; Solides élastiques -- Périodiques; Elastic solids; Mechanics, Applied; Structural analysis (Engineering); Periodicals; 624.18
• DOI: 10.1016/j.ijsolstr.2016.10.023
• Languages: English
• ISSNs: 0020-7683

Abstract

Abstract: In this paper, we focus on replacement relation that links the property contribution tensors of inhomogeneities having the same shape but different elastic properties. We check the possibility to apply the relations, originally derived for ellipsoidal inhomogeneities (Sevostianov & Kachanov 2007) to ones of non-ellipsoidal shape. We discuss inhomogeneities of superspherical shape, described by equation x 2 p + y 2 p + z 2 p ≤ 1 and show that the replacement relations can be used in the rank of convex shapes ( p > 0.5), while for concave shapes the error is significant. In practical applications, it means that for materials with convex inhomogeneities results obtained for effective elastic constants of a porous material can be used to approximately evaluate effective properties of a composite of the same morphology.