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Part of the book series: IUTAM BookSeries ((IUTAMBOOK,volume 11))

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Abstract

A conserved energy and a Hamiltonian is constructed for linear hereditary viscoelastic bodies whose relaxation moduli are positive definite. The Hamiltonian represents an elastic field interacting with a system of uncoupled oscillators.

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References

  1. S. Breuer and E.T. Onat. On the determination of free energy in viscoelastic solids. ZAMP, 15:185–191, 1964.

    Article  Google Scholar 

  2. M. Fabrizio and A. Morro. Mathematical Problems in Linear Viscoelasticity. SIAM, Philadelphia, 1992.

    MATH  Google Scholar 

  3. B.U. Felderhof. On the derivation of the Fluctuation-Dissipation Theorem. Journal of Physics A: Mathematical and General, 11:921–927, 1978.

    Article  MathSciNet  Google Scholar 

  4. F.W. Ford, J.T. Lewis, and R.F. O’Connell. Independent oscillator model of a heat bath: Exact diagonalization of the Hamiltonian. Journal of Statistical Physics, 53:439–455, 1988.

    Article  MathSciNet  Google Scholar 

  5. Y.C. Fung. Biomechanics. Mechanical Properties of Living Tissues. Springer-Verlag, New York, 1981.

    Google Scholar 

  6. G. Gripenberg, S.O. Londen, and O.J. Staffans. Volterra Integral and Functional Equations. Cambridge University Press, Cambridge, 1990.

    MATH  Google Scholar 

  7. A. Hanyga. Viscous dissipation and completely monotone stress relaxation functions. Rheologica Acta, 44:614–621, 2005. doi:10.1007/s00397-005-0443-6.

    Article  Google Scholar 

  8. A. Hanyga and M. Seredyfiska. Hamiltonian and Lagrangian theory of viscoelasticity. Continuum Mechanics and Thermodynamics, 19:475–492, 2008. doi: 10.1007/s00161-007-0065-6.

    Article  MathSciNet  MATH  Google Scholar 

  9. A. Hanyga and M. SeredyƄska. On a mathematical framework for dielectric relaxation functions. Journal of Statistical Physics, 131:269–303, 2008. doi: 10.1007/s10955-008-9501-7.

    Article  MATH  MathSciNet  Google Scholar 

  10. A. Hanyga and M. SeredyƄska. Relations between relaxation modulus and creep compliance in anisotropic linear viscoelasticity. Journal of Elasticity, 88:41–61, 2007.

    Article  MATH  Google Scholar 

  11. R. Kubo, N. Toda, and N. Hashitsune. Statistical Physics II: Nonequilibrium Statistical Physics. Springer-Verlag, Berlin, 1991. 2nd edition.

    MATH  Google Scholar 

  12. A. Molinari. ViscoĂ©lasticitĂ© linĂ©aire and functions complĂštement monotones. Journal de MĂ©canique, 12:541–553, 1975.

    MathSciNet  Google Scholar 

  13. P. J. Morrison. Hamiltonian description of an ideal fluid. Reviews of Modern Physics, 70:467–521, 1998.

    Article  MathSciNet  Google Scholar 

  14. M. SeredyƄska and A. Hanyga. Nonlinear 2dof pendulum with fractional damping. Acta Mechanica, 176:169–183, 2005. doi:10.1007/s00707-005-0220-8.

    Article  MATH  Google Scholar 

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Hanyga, A., SeredyƄska, M. (2008). Hamiltonian Theory of Viscoelasticity. In: Reddy, B.D. (eds) IUTAM Symposium on Theoretical, Computational and Modelling Aspects of Inelastic Media. IUTAM BookSeries, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9090-5_34

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  • DOI: https://doi.org/10.1007/978-1-4020-9090-5_34

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-9089-9

  • Online ISBN: 978-1-4020-9090-5

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