Lagrangian

On Rationally Complete Algebraic Systems of Finite Strain Tensors of Complex Continua

Authors: Kovalev V. A., Radaev Y. N.

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.

Rotational Invariance of Non-Linear Lagrangians of Type-II Micropolar Thermoelastic Continuum

Authors: Radaev Y. N.
The paper contains new results related to extension of the field theoretical approach and its formalism to non-linear coupled
micropolar thermoelastic media. A mathematical model of micropolar (MP) type-II (GNII) thermoelastic (TE) continuum is considered.
A formulation of the least thermoelastic action principle is discussed. Partial differential equations subsequent to the least action
principle are derived. The translational symmetries of non-linear Lagrangians are adopted. Those include an additional symmetry:

Covariant field equations and d-tensors of hyperbolic thermoelastic continuum with fine microstructure

Authors: Kovalev V. A., Radaev Y. N.

A non-linear mathematical model of hyperbolic thermoelastic continuum with fine microstructure is proposed. The model is described in terms of 4-covariant field theoretical formalism. Fine microstructure is represented by d-tensors, playing role of extra field variables. A Lagrangian density for hyperbolic thermoelastic continuum with fine microstructure is given and the corresponding least action principle is formulated. 4-covariant field equations of hyperbolic thermoelasticity are obtained. Constitutive equations of microstructural hyperbolic thermoelasticity are discussed.