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Elastic materials with coincident principal stress and strain axes. (English) Zbl 0818.73014

Summary: A representation is derived for a Cauchy stress response function that is necessary and sufficient for a simple material without memory to 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 nessecarily isotropic.

MSC:

74B99 Elastic materials
74B20 Nonlinear elasticity
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References:

[1] C. Truesdell and W. Noll, The nonlinear field theories of mechanics. In S. Flügge (ed.), Handbuch der Physik, Vol. III/3. Berlin: Springer-Verlag (1985). · Zbl 0779.73004
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