Invariance relations in thermoelasticity with generalized variables

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Abstract
In the spirit of generalized coordinates in Lagrangian mechanics, the finite deformation of a material element is considered to be specified by arbitrary geometric variables, and the associated generalized stresses are generated by work conjugacy. The comparative quantitative influences of such coordinate choices are investigated for the main state variables in anisotropic thermoelasticity, namely the moduli, compliances, thermal coefficients of expansion, pressure coefficients, and specific heats. Transformation formulae are obtained to connect the respective values of the state variables for different choices. Special attention is given to the identification of coordinate-invariant magnitudes and relationships. The entire analysis is carried farther for coordinates in a class of tensor measures of finite strain; such measures are used widely in current theories of the mechanical response of solid materials, but apparently not yet in regard to thermal phenomena.

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