On an extended Hamilton principle for electro/magneto-thermo-mechanical materials with dissipative microstructure evolution

An important part for material modeling is the consideration of electromagnetic fields. In this paper, we add them to Hamilton’s principle for mechanical and thermal fields. We begin with a brief introduction to the electric and magnetic limit cases, which allows a non-relativistic formulation. After introducing the thermodynamic fundamentals, we present the Hamilton functionals for the limit cases from which we derive our governing system of equations by applying Hamilton’s principle of stationary action. In order to be able to describe the microstructure as well, we also consider general internal variables. After the derivation of the equations for the dominant fields, we show how to obtain the secondary fields. For both limit cases we show an example where the dominant electromagnetic field and the mechanic field are coupled by material properties.