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Dissipative Systems in Contact with a Heat Bath: Application to Andrade Creep

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IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials

Part of the book series: IUTAM Bookseries ((IUTAMBOOK,volume 21))

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Abstract

We develop a theory of statistical mechanics for dissipative systems governed by equations of evolution that assigns probabilities to individual trajectories of the system. The theory is made mathematically rigorous and leads to precise predictions regarding the behavior of dissipative systems at finite temperature. Such predictions include the effect of temperature on yield phenomena and rheological time exponents. The particular case of an ensemble of dislocations moving in a slip plane through a random array of obstacles is studied numerically in detail. The numerical results bear out the analytical predictions regarding the mean response of the system, which exhibits Andrade creep.

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Author information

Authors and Affiliations

  1. Mathematics Institute, Warwick University, Coventry, CV47AL, United Kingdom

    Florian Theil & Tim Sullivan

  2. School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN, 47907-2088, U.S.A.

    Marisol Koslovski

  3. Engineering and Applied Sciences Division, California Institute of Technology, Pasadena, CA, 91125, U.S.A.

    Michael Ortiz

Authors
  1. Florian Theil
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  2. Tim Sullivan
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  3. Marisol Koslovski
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  4. Michael Ortiz
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Corresponding author

Correspondence to Florian Theil .

Editor information

Editors and Affiliations

  1. LS Allgemeine Mechanik, Universität Bochum, Bochum, Germany

    Klaus Hackl

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Theil, F., Sullivan, T., Koslovski, M., Ortiz, M. (2010). Dissipative Systems in Contact with a Heat Bath: Application to Andrade Creep. In: Hackl, K. (eds) IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials. IUTAM Bookseries, vol 21. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9195-6_20

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  • DOI: https://doi.org/10.1007/978-90-481-9195-6_20

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-9194-9

  • Online ISBN: 978-90-481-9195-6

  • eBook Packages: EngineeringEngineering (R0)

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