A note on the Cauchy relations. (English) Zbl 0804.73001
Summary: The Cauchy relations originated in the context of the molecular theory of elasticity. Assuming them implies a reduction of the independent elastic constants which characterize the constitutive tensor in the linear anisotropic case. This paper brings to light a property of the elastic tensor through its decomposition into a symmetric part and into a skew part in the 2nd and 3rd indices. The skew part, which vanishes if and only if the Cauchy relations hold, is connected with a self-equilibrated stress field. The isotropic case is examined as a particular example.
Keywords:
elastic tensor; decomposition; symmetric part; skew part; self- equilibrated stress field; isotropic caseReferences:
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