Thermalization of rate-independent processes by entropic regularization

T. J. Sullivan; M. Koslowski; F. Theil; Michael Ortiz

doi:10.3934/dcdss.2013.6.215

Article Contents

2013, Volume 6, Issue 1: 215-233. Doi: 10.3934/dcdss.2013.6.215

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Thermalization of rate-independent processes by entropic regularization

1.
Applied & Computational Mathematics and Graduate Aerospace Laboratories, California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125-9400
2.
School of Mechanical Engineering, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907-2088
3.
Mathematics Institute, University of Warwick, Coventry, CV4 7AL
4.
Graduate Aerospace Laboratories, California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125

Received: May 2011

Revised: July 2011

Published: February 2013

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Abstract

We consider the effective behaviour of a rate-independent process when it is placed in contact with a heat bath. The method used to ``thermalize'' the process is an interior-point entropic regularization of the Moreau--Yosida incremental formulation of the unperturbed process. It is shown that the heat bath destroys the rate independence in a controlled and deterministic way, and that the effective dynamics are those of a non-linear gradient descent in the original energetic potential with respect to a different and non-trivial effective dissipation potential.

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Mathematics Subject Classification: Primary: 47J35, 82C35.

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