Spectral Decomposition of the Elasticity Tensor

[+] Author and Article Information
S. Sutcliffe

Department of Civil Engineering, Tufts University, Medford, MA 02155

J. Appl. Mech 59(4), 762-773 (Dec 01, 1992) (12 pages) doi:10.1115/1.2894040 History: Received July 05, 1991; Revised November 18, 1991; Online March 31, 2008


The elasticity tensor in anisotropic elasticity can be regarded as a symmetric linear transformation on the nine-dimensional space of second-order tensors. This allows the elasticity tensor to be expressed in terms of its spectral decomposition. The structures of the spectral decompositions are determined by the sets of invariant subspaces that are consistent with material symmetry. Eigenvalues always depend on the values of the elastic constants, but the eigenvectors are, in part, independent of these values. The structures of the spectral decompositions are presented for the classical symmetry groups of crystallography, and numerical results are presented for representative materials in each group. Spectral forms for the equilibrium equations, the acoustic tensor, and the stored energy function are also derived.

Copyright © 1992 by The American Society of Mechanical Engineers
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