Spectral decomposition of anisotropic elasticity

2001 ◽  
Vol 150 (3-4) ◽  
pp. 237-261 ◽  
Author(s):  
P. S. Theocaris ◽  
D. P. Sokolis
Keyword(s):  
Spectral Decomposition ◽  
Anisotropic Elasticity

Spectral Decomposition of the Elasticity Tensor

1992 ◽  
Vol 59 (4) ◽  
pp. 762-773 ◽  
Author(s):  
S. Sutcliffe
Keyword(s):  
Spectral Decomposition ◽  
Dimensional Space ◽  
Anisotropic Elasticity ◽  
Elasticity Tensor ◽  
Symmetry Groups ◽  
Stored Energy ◽  
Equilibrium Equations ◽  
Classical Symmetry ◽  
Spectral Decompositions ◽  
Acoustic Tensor

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.

HORIZON SLICE OF BANDWIDTH-ENHANCED SEISMIC DATA FOR THIN BEDS AUTOTRACKED FROM SPECTRAL DECOMPOSITION

2017 ◽  
Author(s):  
Hyeonju Kim ◽  
◽  
Gwang H. Lee ◽  
Han-J. Kim ◽  
John D. Pigott
Keyword(s):  
Seismic Data ◽  
Spectral Decomposition

Anisotropic Elasticity

1996 ◽  
Author(s):  
T. T. C. Ting
Keyword(s):  
Composite Materials ◽  
Elastic Constants ◽  
Piezoelectric Materials ◽  
Anisotropic Materials ◽  
Anisotropic Elasticity ◽  
Stress Singularities ◽  
Comprehensive Survey ◽  
The Subject ◽  
Key Topics ◽  
First Time

Anisotropic Elasticity offers for the first time a comprehensive survey of the analysis of anisotropic materials that can have up to twenty-one elastic constants. Focusing on the mathematically elegant and technically powerful Stroh formalism as a means to understanding the subject, the author tackles a broad range of key topics, including antiplane deformations, Green's functions, stress singularities in composite materials, elliptic inclusions, cracks, thermo-elasticity, and piezoelectric materials, among many others. Well written, theoretically rigorous, and practically oriented, the book will be welcomed by students and researchers alike.

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