Instabilities of a thermo-mechano-chemical system
Author:
Xanthippi Markenscoff
Journal:
Quart. Appl. Math. 59 (2001), 471-477
MSC:
Primary 35B35; Secondary 35B40, 35Q72, 35R25
DOI:
https://doi.org/10.1090/qam/1848529
MathSciNet review:
MR1848529
Full-text PDF Free Access
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Abstract: A Hadamard instability analysis of the partial differential equations governing a coupled thermo-mechano-chemical system predicts instability of the spinoidal decomposition type as well as instability of the “negative creep” type.
J. W. Cahn and John E. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy, J. Chemical Phys. 28, 258–267 (1958)
J. C. M. Li, Negative creep and mechanochemical spinoidal in amorphous metals, Materials Science and Engineering 98, 465–468 (1988)
E. Girt, P. Tomic, I. Gazdic, and T. Mihac, The relaxation of $Cu_{60}Zr_{40}$ metallic glass under tensile stress, J. Phys. F. 13, 747–751 (1983)
P. T. Vianco, Creep and structural relaxation of amorphous metals, Ph.D. Thesis, University of Rochester, Rochester, NY, 1986
- R. M. Bowen, Toward a thermodynamics and mechanics of mixtures, Arch. Rational Mech. Anal. 24 (1967), no. 5, 370–403. MR 1553491, DOI https://doi.org/10.1007/BF00253154
F. C. Larché and J. W. Cahn, The interactions of composition and stress in crystalline solids, Acta Metall. 33, 331–357 (1985)
I. Mueller, Thermodynamics, Pitman, London, 1985
- Xanthippi Markenscoff, Diffusion induced instability, Quart. Appl. Math. 59 (2001), no. 1, 147–151. MR 1811099, DOI https://doi.org/10.1090/qam/1811099
J. W. Cahn and John E. Hilliard, Free energy of a nonuniform system. I. Interfacial free energy, J. Chemical Phys. 28, 258–267 (1958)
J. C. M. Li, Negative creep and mechanochemical spinoidal in amorphous metals, Materials Science and Engineering 98, 465–468 (1988)
E. Girt, P. Tomic, I. Gazdic, and T. Mihac, The relaxation of $Cu_{60}Zr_{40}$ metallic glass under tensile stress, J. Phys. F. 13, 747–751 (1983)
P. T. Vianco, Creep and structural relaxation of amorphous metals, Ph.D. Thesis, University of Rochester, Rochester, NY, 1986
R. M. Bowen, Toward a thermodynamics and mechanics of mixtures, Arch. Rat. Mech. Anal. 24, 370–403 (1967)
F. C. Larché and J. W. Cahn, The interactions of composition and stress in crystalline solids, Acta Metall. 33, 331–357 (1985)
I. Mueller, Thermodynamics, Pitman, London, 1985
X. Markenscoff, Diffusion induced instability, Quart. Appl. Math. 59, 147–151 (2001)
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Article copyright:
© Copyright 2001
American Mathematical Society
