On Thermal Effects in the Theory of Rods.
CALIFORNIA UNIV BERKELEY DEPT OF MECHANICAL ENGINEERING
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This paper is concerned with thermomechanics of slender rods by a direct approach based on the theory of a Cosserat curve comprising a one-dimensional curve and a pair of directors attached to every point of the curve. In all previous developments of the thermomechanical theory of rods by direct approach, only one temperature field has been admitted. This allows for the characterization of temperature changes along some reference curve, such as the line of centroids of the three-dimensional rod-like body, but not the temperature changes across the rod cross-section. A main purpose of the present study is to incorporate the latter effect into the theory and, in the context of the theory of a Cosserat curve to thermomechanics which provides a natural way to introducing more than one temperature field at each material point of the curve. Apart from full discussion of thermomechanics of rods and thermodynamical restrictions arising from the second law of thermodynamics for rods, attention is given to a discussion of symmetries including material symmetries of rods which in a reference configuration are straight.