Dynamic equations of thermoelastic Cosserat rods

A thermoelastic Cosserat rod with a heat flux along its length is modeled after reviewing a simple Cosserat rod model. Extended Kirchhoff constitutive relations that include thermal effects, and the associated heat conduction equation, are derived using the first law of thermodynamics. The rate of internal dissipation of the Cosserat rod is estimated by the Clausius–Duhem inequality. Nonlinear dynamic equations of the thermoelastic Cosserat rod, which extend the simple Cosserat rod model, are obtained. Dynamic equations of a planar thermoelastic Cosserat rod, the Timoshenko thermoelastic beam, and the planar Euler–Bernoulli thermoelastic beam are derived as a special case within the framework of the thermoelastic Cosserat rod.