TY - JOUR

T1 - Violations of the Clausius-Duhem inequality in Couette flows of granular media

T2 - Violations of Clausius-Duhem inequality

AU - Ostoja-Starzewski, Martin

AU - Laudani, Rossella

N1 - Funding Information:
Data accessibility. This article has no additional data. Authors’ contributions. M.O.-S. conceived of and designed the study. M.O.-S. has primarily contributed to §2, while R.L. to §3. R.L. made all the figures. M.O.-S. primarily drafted the manuscript, which both authors then approved. Competing interests. We declare we have no competing interests. Funding. The work of M.O.-S. was funded in part, by the National Institute of Biomedical Imaging and Bioengineering of the NIH under award R01EB029766. R.L. acknowledges support by the University of Messina. Acknowledgements. M.O.-S. acknowledges hospitality of L. Margolin during a visit at Los Alamos National Laboratories, when a part of this research was performed. Expert comments on LAMMPS by S.J. Plimpton (Sandia National Laboratories) and on Couette flows by R.E. Khayat (University of Western Ontario) are appreciated.
Publisher Copyright:
© 2020 The Author(s).

PY - 2020/12

Y1 - 2020/12

N2 - Spontaneous violations of the Clausius-Duhem (CD) inequality in Couette-type collisional flows of model granular media are studied. Planar systems of monosized circular discs (with disc numbers from 10 to 204, and disc diameters from 0.001 m to 1 m) with frictional-Hookean contacts are simulated under periodic boundary conditions by a molecular dynamics. The scale-dependent homogenization of micropolar media is used to determine the energy balances and mechanical entropy production. The dissipation function exhibits spontaneous negative entropy increments described by the fluctuation theorem. The boundary between violations and non-violations of the CD inequality is mapped in the parameter space, where the probability of such events diminishes with the disc diameter, the disc number and the area fraction increasing. The dissipation function is a random process, tending to Gaussian as the number of discs increases, and possessing non-trivial fractal and anti-persistent Hurst properties.

AB - Spontaneous violations of the Clausius-Duhem (CD) inequality in Couette-type collisional flows of model granular media are studied. Planar systems of monosized circular discs (with disc numbers from 10 to 204, and disc diameters from 0.001 m to 1 m) with frictional-Hookean contacts are simulated under periodic boundary conditions by a molecular dynamics. The scale-dependent homogenization of micropolar media is used to determine the energy balances and mechanical entropy production. The dissipation function exhibits spontaneous negative entropy increments described by the fluctuation theorem. The boundary between violations and non-violations of the CD inequality is mapped in the parameter space, where the probability of such events diminishes with the disc diameter, the disc number and the area fraction increasing. The dissipation function is a random process, tending to Gaussian as the number of discs increases, and possessing non-trivial fractal and anti-persistent Hurst properties.

KW - Clausius-Duhem inequality

KW - Couette flow

KW - continuum mechanics

KW - entropy production inequality

KW - fluctuation theorem

KW - granular media

UR - http://www.scopus.com/inward/record.url?scp=85097650175&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85097650175&partnerID=8YFLogxK

U2 - 10.1098/rspa.2020.0207rspa20200207

DO - 10.1098/rspa.2020.0207rspa20200207

M3 - Article

AN - SCOPUS:85097650175

VL - 476

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0080-4630

IS - 2244

M1 - 20200224

ER -