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Anisotropic ElasticityTheory and Applications$
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T. T. C. Ting

Print publication date: 1996

Print ISBN-13: 9780195074475

Published to Oxford Scholarship Online: November 2020

DOI: 10.1093/oso/9780195074475.001.0001

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The Stroh Formalism

The Stroh Formalism

Chapter:
(p.134) Chapter 5 The Stroh Formalism
Source:
Anisotropic Elasticity
Author(s):

T. C. T. Ting

Publisher:
Oxford University Press
DOI:10.1093/oso/9780195074475.003.0008

In this chapter we study Stroh’s sextic formalism for two-dimensional deformations of an anisotropic elastic body. The Stroh formalism can be traced to the work of Eshelby, Read, and Shockley (1953). We therefore present the latter first. Not all results presented in this chapter are due to Stroh (1958, 1962). Nevertheless we name the sextic formalism after Stroh because he laid the foundations for researchers who followed him. The derivation of Stroh’s formalism is rather simple and straightforward. The general solution resembles that obtained by the Lekhnitskii formalism. However, the resemblance between the two formalisms stops there. As we will see in the rest of the book, the Stroh formalism is indeed mathematically elegant and technically powerful in solving two-dimensional anisotropic elasticity problems. The possibility of extending the formalism to three-dimensional deformations is explored in Chapter 15.

Keywords:   Airy function, Barnett-Lothe tensors, Dundurs constants, Eshelby-Reid-Shockley formalism, Hermitian, Jordan canonical form, closure relations, degenerate materials, eigenplane

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