Rotational invariance of non-linear Lagrangians of type-II micropolar thermoelastic continuum

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: translations of the thermal displacement. The rotational invariance of the action and corresponding Lagrangian is then studied. For micropolar type-II thermoelastic Lagrangians following the usual procedure independent rotationally invariant functional arguments are obtained. Objective forms of the Lagrangians satisfying the frame indifference principle are given.