On thermodynamically consistent form of nonlinear equations of the cosserat theory

• Autorzy: Sadovskii V.
• Języki publikacji: EN

Abstrakty

EN

To describe motion in a micropolar medium a special measure of curvature is used that is a strain state characteristic independent of deformation process. The nonlinear constitutive equations of the couple stress theory are constructed using the method of internal thermodynamic parameters of state. The linearization of these equations in isotropic case yields the Cosserat continuum equations, where material resistance to the change in curvature is characterized by a single coefficient as against three independent coefficients of the classical theory. So, it turns out that the developed variant of the model gives an adequate description of generalized plane stress state in an isotropic micropolar medium, while the classical one describes this state only at a certain case. The complete system of nonlinear equations for the dynamics of a medium with couple stresses reduces to a thermodynamically consistent system of laws of conservation, which allows obtaining integral estimates that guarantee the correctness of the Cauchy problem and boundary-value problems with dissipative boundary conditions.

Słowa kluczowe

EN

cosserat continuum; curvature tensor; thermodynamically consistent system

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Engineering Transactions
• Rocznik: 2017
• Tom: Vol. 65, iss. 1
• Strony: 201--208
• Opis fizyczny: Bibliogr. 7 poz., rys.

Twórcy

autor

Sadovskii V.

• Institute of Computational Modeling SB RAS Krasnoyarsk, Russia

Bibliografia

• 1. Pal’mov V.A., Fundamental equations of the theory of asymmetric elasticity, J. Appl. Math. Mech., 28(3): 496–505, 1964.
• 2. Nikitin E., Zubov L.M., Conservation laws and conjugate solutions in the elasticity of simple materials and materials with couple stress, J. Elast., 51: 1–22, 1998.
• 3. Pietraszkiewicz W., Eremeev V.A., On natural strain measures of the non-linear micropolar continuum, Int. J. Solids Struct., 46: 774–787, 2009.
• 4. Godunov S.K., Romenskii E.I., Elements of Continuum Mechanics and Conservation Laws, Kluwer Academic/Plenum Publishers, New York – Boston – Dordrecht – London – Moscow, 2003.
• 5. Sadovskaya O., Sadovskii V., Mathematical Modeling in Mechanics of Granular Materials, Ser.: Advanced Structured Materials, 21, Springer, Heidelberg – New York – Dordrecht – London, 2012.
• 6. Kondaurov V.I., Non-linear equations of the dynamics of an elastic micropolar medium, J. Appl. Math. Mech., 48(3): 291–299, 1984.
• 7. Sadovskii V.M., Thermodynamically consistent system of conservation laws of nonsymmetric elasticity theory [in Russian], Dal’nevost. Mat. Zh., 11(2): 201–212, 2011.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).