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Elastic materials with coincident principal stress and strain axes

โœ Scribed by Janet A. Blume

Publisher
Springer Netherlands
Year
1994
Tongue
English
Weight
179 KB
Volume
35
Category
Article
ISSN
0374-3535

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โœฆ Synopsis

In this note, a representation is derived for a Cauchy stress response function that is necessary and sufficient in order that a simple material without memory be such that the principal axes of strain and stress always coincide. It is found that the material need not be isotropic. However, if the material is in addition hyperelastic, so that the work done in any cyclic motion is zero, it is shown that the material is necessarily isotropic.

1. Formulation

A body occupies a region R in a reference configuration. A motion of the body is described by a suitably smooth and invertible mapping y = ~'(x, t)

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