Geodesic
The Lagrange multipliers method in covariant formulations of micropolar continuum mechanics theories
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 22 (2018) no. 3, pp. 504-517.

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Linear model of micropolar elastic continuum (known also as the Cosserat continuum) is considered. Kinematics and strain measures are discussed. The symmetric small strains tensor, relative microrotation vector and spatial gradient of the total microrotation vector (the wryness tensor) are then employed for a covariant formulation of the micropolar theory. By means of the principle of virtual displacements much simplified by the lack of internal forces and couples contributions to the virtual work and the Lagrange multipliers method the micropolar theory of elasticity is developed. Hemitropic micropolar continuum model is investigated in further details. The paper is to be considered as a universal covariant script of equations of the linear micropolar theory of elasticity derived from the virtual displacements principle.
Keywords: micropolar continuum, couple stress, virtual displacements principle, virtual work
Mots-clés : force stress, Lagrange multipliers, covariant formulation. 
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Yu. N. Radayev. The Lagrange multipliers method in covariant formulations of micropolar continuum mechanics theories. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 22 (2018) no. 3, pp. 504-517. http://geodesic.mathdoc.fr/item/VSGTU_2018_22_3_a5/

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