On the behavior of dissipative systems in contact with a heat bath: Application to Andrade creep
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.
© 2009 Elsevier. Received 26 November 2008; revised 16 March 2009; accepted 21 March 2009. Available online 1 April 2009. The support of the DoE through Caltech's PSAAP Center for the Predictive Modeling and Simulation of High-Energy Density Dynamic Response of Materials is gratefully acknowledged. TJS' research is supported by the EPSRC and University of Warwick Research Development Fund.