  An established strategy for material modeling is provided by energy-based
principles such that evolution equations in terms of ordinary differential
equations can be derived. However, there exist a variety of material models
that also need to take into account non-local effects to capture microstructure
evolution. In this case, the evolution of microstructure is described by a
partial differential equation. In this contribution, we present how Hamilton's
principle provides a physically sound strategy for the derivation of transient
field equations for all state variables. Therefore, we begin with a
demonstration how Hamilton's principle generalizes the principle of stationary
action for rigid bodies. Furthermore, we show that the basic idea behind
Hamilton's principle is not restricted to isothermal mechanical processes. In
contrast, we propose an extended Hamilton principle which is applicable to
coupled problems and dissipative microstructure evolution. As example, we
demonstrate how the field equations for all state variables for
thermo-mechanically coupled problems, i.e. displacements, temperature, and
internal variables, result from the stationarity of the extended Hamilton
functional. The relation to other principles, as principle of virtual work and
Onsager's principle, are given. Finally, exemplary material models demonstrate
how to use the extended Hamilton principle for thermo-mechanically coupled
rate-dependent, rate-independent, and gradient-enhanced materials.
