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New variational principles in quasi-static viscoelasticity

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Abstract

A “saddle point” (or maximum-minimum) principle is set up for the quasi-static boundary-value problem in linear viscoelasticity. The appropriate class of convolution-type functionals for it is taken in terms of bilinear forms with a weight function involving the Fourier transform. The “minimax” property is shown to hold as a direct consequence of thermodynamic restrictions on the relaxation function. This approach can be extended to further linear evolution problems where initial data are not prescribed.

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References

  1. R.M. Christensen, Theory of Viscoelasticity, 2nd edn. New York: Academic Press (1982).

    Google Scholar 

  2. M. Ciarletta and E. Scarpetta, Minimum problems in the dynamics of viscous fluids with memory. Int. J. Engng. Sci. 27 (1989) 1563.

    Google Scholar 

  3. M. Fabrizio, An existence and uniqueness theorem in quasi-static viscoelasticity. Quart. Appl. Math. 47 (1989) 1.

    Google Scholar 

  4. M. Fabrizio and A. Morro, On uniqueness in linear viscoelasticity. A family of counterexamples. Quart. Appl. Math. 45 (1987) 321.

    Google Scholar 

  5. M. Fabrizio and A. Morro, Viscoelastic relaxation functions compatible with thermodynamics. J. Elasticity 19 (1988) 63.

    Google Scholar 

  6. M. Fabrizio, C. Giorgi and A. Morro, Minimum principles, convexity, and thermodynamics in linear viscoelasticity. Continuum Mech. Thermodyn. 1 (1989) 197.

    Google Scholar 

  7. C. Giorgi and B. Lazzari, Uniqueness and stability in linear viscoelasticity: some counterex-amples. to appear in “Proceedings of the Vth International Conference on Waves and Stability in Continuous Media (Sorrento, October 9–14, 1989)”.

  8. B. Lazzari and E. Vuk, Un teorema di esistenza e unicità per un problema dinamico in viscoelasticità lineare. Atti Sem. Mat. Fis. Univ. Modena 35 (1987) 309.

    Google Scholar 

  9. R. Reiss, Minimum principles for linear elastodynamics. J. Elasticity 8 (1978) 35.

    Google Scholar 

  10. R. Reiss and E.J. Haug, Extremum principles for linear initial-value problems of mathematical physics. Int. J. Engng. Sci. 16 (1978) 231.

    Google Scholar 

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Authors and Affiliations

  1. Dipartimento di Matematica, Università Cattolica del S. Cuore, Via Trieste 17, 25121, Brescia, Italy

    C. Giorgi & A. Marzocchi

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  1. C. Giorgi
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  2. A. Marzocchi
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Giorgi, C., Marzocchi, A. New variational principles in quasi-static viscoelasticity. J Elasticity 29, 85–96 (1992). https://doi.org/10.1007/BF00043446

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  • DOI: https://doi.org/10.1007/BF00043446

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