Orthotropic transform for planar anisotropic elasticity and reduced dependence of elastic constants
Resource
Proceeding Royal Society of London, Series A 454: 1843-1855
Journal
Proceeding Royal Society of London, Series A
Journal Volume
454
Journal Issue
1975
Pages
-
Date Issued
1998
Date
1998
Author(s)
Yang, Wei
Abstract
The resurgence in the literature on the reduced dependence of elastic constants for damaged materials and composites has been largely inspired by the exploration of the stress invariance under a modulus shift by Cherkeav and others in 1992 (henceforth referred to as the CLM shift) in planar elasticity. However, a CLM shift can at most reduce the dependence of two elastic constants. The present work devises an approach that combines the CLM shift and an orthotropic transform. As a result, the governing equation of a general planar anisotropic solid only contains a single dimensionless elastic constant (denoted by |c£| in this paper) in the transformed coordinates. The damage compliance of a solid with holes can be expressed explicitly through a function depending only on |c*2|. If an elastic composite consists of a matrix and inclusions of aligned anisotropy, its overall compliance can be expressed through a function of three combinative parameters, namely |c%| and two Dundurs parameters. Furthermore, a configuration invariant transform is found for layered materials of aligned anisotropy. The stress analysis of such configurations only involves four elastic constants. © 1998 The Royal Society.
Subjects
Elastic constants; Holes; Inclusions; Layered materials; Orthotropic transform; Planar anisotropy
SDGs
Type
journal article
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