Technical Briefs

On Thermodynamic Restrictions in Peridynamics

[+] Author and Article Information
M. Ostoja-Starzewski

Department of Mechanical Science & Engineering
also Institute for Condensed Matter Theory
and Beckman Institute
University of Illinois at Urbana-Champaign
Urbana, IL 61801
e-mail: martinos@illinois.edu

P. N. Demmie

Sandia National Laboratories
Albuquerque, NM 87185
e-mail: pndemmi@sandia.gov

A. Zubelewicz

Theoretical Division
Los Alamos National Laboratory
Los Alamos, NM 87545
e-mail: alek@lanl.gov

Manuscript received September 18, 2011; final manuscript received March 20, 2012; accepted manuscript posted June 7, 2012; published online October 29, 2012. Editor: Robert M. McMeeking.

J. Appl. Mech 80(1), 014502 (Oct 29, 2012) (3 pages) Paper No: JAM-11-1336; doi: 10.1115/1.4006945 History: Received September 18, 2011; Revised March 20, 2012; Accepted June 07, 2012

This note examines restrictions imposed by the second law of thermodynamics on peridynamics in both the bond-based and the state-based formulations. Our study was carried out in the framework of thermomechanics with internal variables. In bond-based peridynamics, there are two possible thermomechanical interpretations of the dissipation function. One interpretation only admits a thermodynamic orthogonality of Ziegler, while the other admits powerless forces within a representation theory of Edelen. The latter interpretation is admissible in state-based peridynamics. Since the dissipation function of peridynamics is set up in velocity space, a link to statistical mechanics of irreversible phenomena does not appear possible.

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