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Granular materials posses disorder structures which are the origin of dynamical heterogeneity. On the basis of non-equilibrium thermodynamics, the structure characteristics, complex deformations, and energy dissipations are analysed. Based on the photoelastic tests, the granular elasticity is discussed. The strain increments are classified into three categories. By means of the non-equilibrium thermodynamics, two granular temperatures, Tk, Tc, are introduced as the state variables, which denote the fluctuations of the kinetic energy and the elastic energy, respectively. Further, a two-granular-temperature thermodynamics (i.e. TGT theory) are developed for granular materials. The thermodynamic forces and fluxes are particularly analyzed. TGT theory is also compared with the previous internal variable thermodynamics for sands (IVT theory) developed a few decades ago. It is found that from TGT the Gibbs free energy in the IVT theory can be deduced, and the energy dissipation function can be apparently expressed from TGT theory.
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Keywords:
- granular materials /
- mesoscale structure /
- dynamical heterogeneity /
- non-equilibrium thermodynamics
[1] Einstein A 1956 Investigations on the theory of the Brownian movement (New York: Dover)
[2] Ogawa S, Umemura A, Oshima N 1980 ZAMP 31 483
[3] Haff P K 1983 J Fluid Mech. 134 401
[4] Lun C K K, Savage S B, Jeffrey D J, Chepurniy N 1984 J. Fluid Mech. 140 223
[5] Jenkins J T, Savage S B 1983 Granular Mat. 130 187
[6] Babic M, Shen H H 1989 J. Eng. Mech. 115 1262
[7] Edwards S F, Oakeshott R B S 1989 Physica A 157 1080
[8] Henkes S, O‘Hern C S, Chakraborty B 2007 Phys. Rev. Lett. 99 038002
[9] Tighe B P, Vlugt T J H 2011 J. Stat. Mech. P04002
[10] Tighe B P, Snoeijer J H, Vlugtc T J H, van Hecke M 2010 Soft Mat. 6 2908
[11] Bi Z, Sun Q, Jin F 2011 Granular Mat. 13 503
[12] Sun Q, Song S, Liu J, Fei M, Jin F 2013 Theoret. Appl. Mech. Lett. 3 021008
[13] Sun Q, Jin F, Zhou G D 2013 Granular Mat. 15 119
[14] Onsager L 1931 Phys. Rev 37 405
[15] Prigogine I 1961 Introduction to Thermodynamics of Irreversible Processes (New York: Interscience)
[16] Jou D, Casas-Vazquez J, Lebon G 2010 Extended Irreversible Thermodynamics (4th Ed.) (Berlin: Springer)
[17] Ottinger H C 2005 Beyond Equilibrium Thermodynamics (New York:: Wiley-Interscience)
[18] Collins I F, Houlsby G T 1997 Proceed. Royal Soc. A 453 1975
[19] Houlsby G T, Puzrin A M 2007 Principles of Hyperplasticity: An Approach to Plasticity Theory Based on Thermodynamic Principles (Berlin: Springer)
[20] Xu N 2011 Front. Phys. 6 109
[21] Jiang Y M, Liu M 2009 Granular Mat. 11 139
[22] Liu Z Y, Yang Y 2012 Intermetallics 26 86
[23] Landau L D, Lifshitz E M 1986 Theory of Elasticity (3rd Ed.) (Butterworth-Heinemann)
[24] Rice J R 1971 J. Math Phys. Solids 19 433
[25] Jenkins J T 2006 Phys. Fluids 18 103307
[26] Wang W H 2012 Prog. Mater. Sci. 57 487
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[1] Einstein A 1956 Investigations on the theory of the Brownian movement (New York: Dover)
[2] Ogawa S, Umemura A, Oshima N 1980 ZAMP 31 483
[3] Haff P K 1983 J Fluid Mech. 134 401
[4] Lun C K K, Savage S B, Jeffrey D J, Chepurniy N 1984 J. Fluid Mech. 140 223
[5] Jenkins J T, Savage S B 1983 Granular Mat. 130 187
[6] Babic M, Shen H H 1989 J. Eng. Mech. 115 1262
[7] Edwards S F, Oakeshott R B S 1989 Physica A 157 1080
[8] Henkes S, O‘Hern C S, Chakraborty B 2007 Phys. Rev. Lett. 99 038002
[9] Tighe B P, Vlugt T J H 2011 J. Stat. Mech. P04002
[10] Tighe B P, Snoeijer J H, Vlugtc T J H, van Hecke M 2010 Soft Mat. 6 2908
[11] Bi Z, Sun Q, Jin F 2011 Granular Mat. 13 503
[12] Sun Q, Song S, Liu J, Fei M, Jin F 2013 Theoret. Appl. Mech. Lett. 3 021008
[13] Sun Q, Jin F, Zhou G D 2013 Granular Mat. 15 119
[14] Onsager L 1931 Phys. Rev 37 405
[15] Prigogine I 1961 Introduction to Thermodynamics of Irreversible Processes (New York: Interscience)
[16] Jou D, Casas-Vazquez J, Lebon G 2010 Extended Irreversible Thermodynamics (4th Ed.) (Berlin: Springer)
[17] Ottinger H C 2005 Beyond Equilibrium Thermodynamics (New York:: Wiley-Interscience)
[18] Collins I F, Houlsby G T 1997 Proceed. Royal Soc. A 453 1975
[19] Houlsby G T, Puzrin A M 2007 Principles of Hyperplasticity: An Approach to Plasticity Theory Based on Thermodynamic Principles (Berlin: Springer)
[20] Xu N 2011 Front. Phys. 6 109
[21] Jiang Y M, Liu M 2009 Granular Mat. 11 139
[22] Liu Z Y, Yang Y 2012 Intermetallics 26 86
[23] Landau L D, Lifshitz E M 1986 Theory of Elasticity (3rd Ed.) (Butterworth-Heinemann)
[24] Rice J R 1971 J. Math Phys. Solids 19 433
[25] Jenkins J T 2006 Phys. Fluids 18 103307
[26] Wang W H 2012 Prog. Mater. Sci. 57 487
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