The article is dedicated to the 60th anniversary of professor Yu. N. Radaev, the well-known scientist in the field of mechanics of deformable solids and applied mathematics, the member of the editorial board of the journal “Izvestiya of Saratov University. Mathematics. Mechanics. Informatics”.
The paper is devoted to the 4-covariant formulation in fourdimensional space-time of dynamics of non-linear hyperbolic micropolar thermoelastic continuum. Theory ofmicropolar continuum are due to E. Cosserat and F. Cosserat and their study of 1909. The complement microdeformations and microrotations of an element are described by a non-rigid trihedron (the case of deformable micropolar directors).
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.
The paper is devoted to the mathematical description of complex continua and the systematic derivation of strain tensors by the notion of isometric immersion of complex continuum in a plane space of higher dimension. Problem of establishing of complete systems of irreducible objective strain and extra-strain tensors for complex continuum immersed in an external plane space is considered. The solution to the problem is given by methods of the field theory and the theory of algebraic invariants.
