On KelvinVoigt model and its generalizations
Miroslav Bulíček  Mathematical Institute of Charles University, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Prague, Czech Republic (email) Abstract: We consider a generalization of the KelvinVoigt model where the elastic part of the Cauchy stress depends nonlinearly on the linearized strain and the dissipative part of the Cauchy stress is a nonlinear function of the symmetric part of the velocity gradient. The assumption that the Cauchy stress depends nonlinearly on the linearized strain can be justified if one starts with the assumption that the kinematical quantity, the left CauchyGreen stretch tensor, is a nonlinear function of the Cauchy stress, and linearizes under the assumption that the displacement gradient is small. Longtime and large data existence, uniqueness and regularity properties of weak solution to such a generalized KelvinVoigt model are established for the nonhomogeneous mixed boundary value problem. The main novelty with regard to the mathematical analysis consists in including nonlinear (nonquadratic) dissipation in the problem.
Keywords: KelvinVoigt model, viscoelastic solid, nonlinear wave equation, weak solution, large data existence, uniqueness, regularity.
Received: October 2011; Revised: February 2012; Available Online: March 2012. 
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