Conservation Laws and Material Momentum in Thermoelasticity

The main goal of this paper is to construct a Lagrangian function such that not only the well-known equations of thermoelasticity, but also material conservation laws can be derived. As action variables, the position x of a material particle and a scalar function η related to temperature are used. The material momentum for thermoelasticity is derived. Here, by contrast to the purely elastic case, the material momentum depends on a time interval rather than on an instant of time. The balance of material momentum is integrated over time to produce a relation reminiscent of the impulse-momentum equation in classical mechanics.