Solution of Extended Kelvin-Voigt Model
Sławomir Karaś
Department of Roads and Bridges; Faculty of Civil Engineering and Architecture; Lublin University of Technology (Poland)
https://orcid.org/0000-0002-0626-5582
Abstract
The great usefulness of uniaxial visco-elastic models, especially in highway engineering pavement theory, composites and other civil engineering disciplines were the reason for undertaking the trial to find a complete solution for the generalization of Kelvin-Voigt body. Here the elements of higher rank than velocities of strain and stress are considered. Carson’s transformation simultaneously with residuum theorem are used for solutions derivation. The introduced procedure can be also used for more complicated differential or integral forms of constitutive equations, as well as for non homogenous initial conditions. The Burgers’ body is examined. Finally, as an example the vibration of simple beam is shown.
Keywords:
rheology, visco-elasticity, modelsReferences
Maxwell J.C., On the Dynamical Theory of Gases, Philos. Trans. R. Soc., 1867.
Google Scholar
Voigt W., Abhandlungen der Königlichen Gesellschaft von Wissenschaften zu Göttingen, vol. 36, 1890.
Google Scholar
Thomson W., Math. And Phys. Papers, 3, Cambridge, 1890; (Kelvin W. – Encyclopedia Britannica, v. 3, London, 1875).
Google Scholar
Poynting J.H., Thomson J.J., Properties of Matter, London, 1902.
Google Scholar
Burgers I.M., First Report of Viscosity and Plasticity, Amsterdam, 1935.
Google Scholar
Zener C., Elasticity and Inelasticity of Metals, Chicago, 1948.
Google Scholar
Reiner M., Rheology, edited by S. Flügge Encyclopedia of Physics, Vol. VI, Springer, Berlin-Göttingen-Heidelberg, 1958.
Google Scholar
Nowacki W., Theory of Creep (In Polish), ARKADY. Warszawa, 1963.
Google Scholar
Wang, H.F., Theory of Linear Poroelasticity. Princeton University Press, 2000.
Google Scholar
Detournay E., Dormieux L., Roatesi S., Fourmaintraux D., Stability of a Borehole Drilled in a Chemically Active Shale, BIOT 2002, Poromechanics II, Balkema Publ., 2002, pp. 171-179.
DOI: https://doi.org/10.1201/9781003078807-26
Google Scholar
Nagórski R., Wiśniakowski P., Błażejowski K., Nagórska M., Comparative analysis of Burger’s, Boguslavskis’ and Zener’s materials in view of tests and strain in reference to properties of asphalt mixes, Roads and Bridges 1/2012.
Google Scholar
Maczelski Cy., Toczkiewicy R., Rheological effects in composite beam with sandwich deck slab, Roads and Bridges 1/2007.
Google Scholar
Graczyk M., Rafa J., Selected aspects of the behaviour of flexible pavements in thermoviscoelasticity material models, Roads and Bridges 2/2010.
Google Scholar
Authors
Sławomir KaraśDepartment of Roads and Bridges; Faculty of Civil Engineering and Architecture; Lublin University of Technology Poland
https://orcid.org/0000-0002-0626-5582
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