On thermal effects in the theory of rods

Abstract

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 thermo-mechanical 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 for 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, this is achieved by a recent approach of Green and Naghdi [1,2] to thermomechanics which provides a natural way of 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. The paper also contains a'detailed discussion of the linear theory of straight, elastic, orthotropic rods, including the determination of the relevant constitutive coefficients.