pdf - The World of Mathematical Equations

UDK 532.5: 539.3E 66E 66Eremeyev V. А., Zubov L. М. Principles of viscoelastic micropolarfluid mechanics. Rostov on Don: South Scientific Center of RASci,2009. – 128 pp.In the monograph we present the one model of nonclassical fluid.This model is the viscoelastic micropolar fluid. Within frameworks of theconsidered model each material point of the fluid has the translationaland rotational degrees of freedom and there exist the couple stresses.The characteristic feature of the described model is the property of theorientation elasticity. This property is well-known in the hydromechanicsof liquid crystals. The difference and similarity between the model ofnematic-type liquid crystal and the elastic micropolar fluid are discussed.The micropolar fluid can be subjected by forces and moments distributedin the volume which is occupied by the micropolar fluid and on its surface.The various fading memory properties are considered. The kinematicsof Cosserat continuum is considered in details. The strain measures andwriness tensor are introduced. The theory of stresses in developed. Themotion equations of the Cosserat continuum are deduced. The thermodynamicaltheory of the constitutive equations is considered. The statementsof initial-boundary-value problems are given. The solutions of the selectedproblems of the statics, dynamics, and instability are presented.UDK 532.5: 539.3ISBN 978-5-902982-56-2c○ V. A. Eremeyev, 2009c○ L. M. Zubov, 2009c○ South Scientific Center of RASci, 2009