A local-effective relation in planar linear elasticity. Issue 12 (10th September 2017)

• Record Type: Journal Article
• Authors: Lukkassen, Dag; Meidell, Annette; Pettersson, Klas
• Is Part Of: Mechanics of advanced materials and structures. Volume 24:Issue 12(2017)
• Page Start: 999
• Page End: 1006
• Publication Date: 2017-09-10
• Subjects: Effective elastic properties -- heterogeneous media -- planar linear elasticity; Composite materials -- Mechanical properties -- Periodicals; Composite construction -- Periodicals; 620.118
• DOI: 10.1080/15376494.2016.1201178
• Languages: English
• ISSNs: 1537-6494

Abstract

ABSTRACT: We present a relation between local and effective properties for a class of two-dimensional elastic structures. The model considered is a periodic structure, which is locally isotropic and homogeneous. The corresponding physical model is a flat two-dimensional body with traction-free holes, such as a perforated plate. We show how the effective properties of the structure depend on the local properties in a way that separates the dependence on the holes. Our result extends a result of Vigdergauz [1 ], which describes how effective properties depend on local properties for effectively square symmetric structures, to the case when the effective elasticity tensor is allowed to be anisotropic.