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The Quarterly Journal of Mechanics and Applied Mathematics 1968 21(2):141-146; doi:10.1093/qjmam/21.2.141
© 1968 by Oxford University Press
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A REMARK ON HADAMARD MATERIALS

M. HAYES

( School of Mathematics and Physics, University of East Anglia Nonoich )

The strain energy {Sigma} for Hadamard materials takes the form {Sigma} = aII + bI + f(III). Here a and b are constants, f an arbitrary function, and I, II, III are the principal invariants of the left Cauchy strain tensor. It is shown that if the Ordered Forces condition and the Strong Ellipticity condition are to be satisfied then a = 0, b > 0,f'(III) ≥ 0 and (III1/2f')' ≥ 0.


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