Field theories of the continuum mechanics and physics based on the least action principle are considered in a unified framework. Variation of the action integral in the least action principle corresponds variations of physical fields while space-time coordinates are not varied. However notion of the action invariance, theory of variational symmetries of action and conservation laws require a wider variation procedure including variations of the space-time coordinates.
A new micropolar thermoelastic continuum model forrmulated by microstructural d-vectors and d-tensors of an arbitrary ranks is proposed. The microstructural vectorial and tensorial extra-field variables are restricted by holonomic or non-holonomic (differential) constraints. The study is carried out in the framework of the Lagrange field formalism as a 4covariant field theory.
