On Inconstant Poisson's Ratios in Non-Homogeneous Elastic Media
For non-homogeneous linear elastic materials, it is demonstrated that even for the simplest loading case, i.e. quasi-static uniaxial, the Poisson's ratio (PR) is space dependent and not a constant. Furthermore, the assumption of constant PR values or of separable temporal and spatial
PR functions leads to ill-posed overdetermined problems. Additionally, elastic PRs become space and time dependent under time dependent stresses in non-homogeneous elastic media. Under these and more general circumstances, PRs cannot be considered material property descriptors since they now
become functions of the spatially changing moduli and stresses, and vary accordingly. The same conclusions are also drawn for nonlinear elastic media with small or large deformations.
Keywords: Anisotropic materials; Elasticity; Functionally graded materials; Non-homogeneity; Poisson's ratios; Viscoelastic implications
Document Type: Research Article
Affiliations: 1: Mechanical Engineering Department, Texas A & M University, College Station, Texas, USA 2: Aerospace Engineering Department in the College of Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA
Publication date: 01 January 2010
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