On Hamilton's principle for thermo-elastic fluids and solids, and internal constraints in thermo-elasticity
We have shown here that Hamilton's principle may be used to obtain the equations of motion and to deduce the Cauchy stress principle and the Gibbs relations for one of the simplest models from continuum mechanics, viz., thermo-elastic fluids and solids. We have not limited our theory to isentropic processes; specifically, these models allow for heat conduction. However, we do assume the existence of a thermodynamical potential, but show that the stress and entropy/temperature are obtained from its partial derivatives. Further study will be required to determine whether a similar principle, which is not simply ``little more than a reformulation of the equations of motion'', can be developed for, say, viscous heat-conducting fluids. It is hoped that some of the considerations arising in this work will prove useful in studies of mixtures, liquid crystals, granular solids, etc., where variational principles are sometimes used to obtain equations of motion.
scientific article; zbMATH DE number 4033310
scientific article