54
D. Dudin and I. Keller
of the relaxation times can be associated with the structural schemes integrating the
diffusion and rheological elements. Here, consideration is given to a linear model,
although the method is suitable for studying geometrically and physically nonlinear
equations with the parameters independent of spatial coordinates and time.
The nontrivial result of this study is the conclusion that the elastic strains
depending on the ratio of the characteristic elastic and thermal energies can control the
fast or slow diffusion in a binary metal alloy accompanying the ordinary interdiffusion by the thermal-fluctuation mechanism. The observed fast diffusion is controlled
by a mean stress gradient and is not associated with the microstructure of metal
crystal lattice defects (which is undoubtedly the most important factor responsible
for the activation of the diffusion processes).
Acknowledgements This work was performed in the framework of the state assignment (reg.
No. AAAA-A16-116121410009-8) and under partial financial support by the grant of the Russian
Foundation for Basic Research (project No. 17-08-01085).
References
Alibert, J. J., Seppecher, P., & dell’Isola, F. (2003). Truss modular beams with deformation energy
depending on higher displacement gradients. Mathematics and Mechanics of Solids, 8(1).
Auffray, N., dell’Isola, F., Eremeyev, V., Madeo, A., & Rossi, G. (2013). Analytical continuum
mechanics à la Hamilton-Piola: Least action principle for second gradient continua and capillary
fluids. Mathematics and Mechanics of Solids.
Barchiesi, E., Spagnuolo, M., & Placidi, L. (2018). Mechanical metamaterials: A state of the art.
Mathematics and Mechanics of Solids.
Brassart, L., Liu, Q., & Suo, Z. (2016). Shear, dilation and swap: Mixing in the limit of fast diffusion.
Journal of the Mechanics and Physics of Solids, 96, 48–64.
Brassart, L., Liu, Q., & Suo, Z. (2018). Mixing by shear, dilation, swap and diffusion. Journal of
the Mechanics and Physics of Solids, 112, 253–272.
Darken, L. S. (1948). Diffusion, mobility and their interrelation through free energy in binary
metallic systems. Transactions of the American Institute of Mining, Metallurgical, and Petroleum
Engineers, 175, 184–201.
dell’Isola, F., Seppecher, P., & Madeo, A. (2012). How contact interactions may depend on the shape
of Cauchy cuts in Nth gradient continua: Approach “à la D’Alembert”. Zeitschrift für angewandte
Mathematik und Physik, 63(6).
dell’Isola, F., Andreaus, U., & Placidi, L. (2015). At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical
contribution of Gabrio Piola. Mathematics and Mechanics of Solids, 20(8).
dell’Isola, F., Della, C. A., & Giorgio, I. (2016a). Higher-gradient continua: The legacy of Piola,
Mindlin. Mathematics and Mechanics of Solids: Sedov and Toupin and some future research
perspectives.
dell’Isola, F., Giorgio, I., Pawlikowski, M., & Rizzi, N. (2016b). Large deformations of planar extensible beams and pantographic lattices: Heuristic homogenization, experimental and numerical
examples of equilibrium. Proceedings of The Royal Society A, 472(2185).
dell’Isola, F., Della Corte, A., Greco, L., & Luongo, A. (2016c). Plane bias extension test for
a continuum with two inextensible families of fibers: A variational treatment with Lagrange
multipliers and a perturbation solution. International Journal of Solids and Structures.
D. Dudin and I. Keller
of the relaxation times can be associated with the structural schemes integrating the
diffusion and rheological elements. Here, consideration is given to a linear model,
although the method is suitable for studying geometrically and physically nonlinear
equations with the parameters independent of spatial coordinates and time.
The nontrivial result of this study is the conclusion that the elastic strains
depending on the ratio of the characteristic elastic and thermal energies can control the
fast or slow diffusion in a binary metal alloy accompanying the ordinary interdiffusion by the thermal-fluctuation mechanism. The observed fast diffusion is controlled
by a mean stress gradient and is not associated with the microstructure of metal
crystal lattice defects (which is undoubtedly the most important factor responsible
for the activation of the diffusion processes).
Acknowledgements This work was performed in the framework of the state assignment (reg.
No. AAAA-A16-116121410009-8) and under partial financial support by the grant of the Russian
Foundation for Basic Research (project No. 17-08-01085).
References
Alibert, J. J., Seppecher, P., & dell’Isola, F. (2003). Truss modular beams with deformation energy
depending on higher displacement gradients. Mathematics and Mechanics of Solids, 8(1).
Auffray, N., dell’Isola, F., Eremeyev, V., Madeo, A., & Rossi, G. (2013). Analytical continuum
mechanics à la Hamilton-Piola: Least action principle for second gradient continua and capillary
fluids. Mathematics and Mechanics of Solids.
Barchiesi, E., Spagnuolo, M., & Placidi, L. (2018). Mechanical metamaterials: A state of the art.
Mathematics and Mechanics of Solids.
Brassart, L., Liu, Q., & Suo, Z. (2016). Shear, dilation and swap: Mixing in the limit of fast diffusion.
Journal of the Mechanics and Physics of Solids, 96, 48–64.
Brassart, L., Liu, Q., & Suo, Z. (2018). Mixing by shear, dilation, swap and diffusion. Journal of
the Mechanics and Physics of Solids, 112, 253–272.
Darken, L. S. (1948). Diffusion, mobility and their interrelation through free energy in binary
metallic systems. Transactions of the American Institute of Mining, Metallurgical, and Petroleum
Engineers, 175, 184–201.
dell’Isola, F., Seppecher, P., & Madeo, A. (2012). How contact interactions may depend on the shape
of Cauchy cuts in Nth gradient continua: Approach “à la D’Alembert”. Zeitschrift für angewandte
Mathematik und Physik, 63(6).
dell’Isola, F., Andreaus, U., & Placidi, L. (2015). At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical
contribution of Gabrio Piola. Mathematics and Mechanics of Solids, 20(8).
dell’Isola, F., Della, C. A., & Giorgio, I. (2016a). Higher-gradient continua: The legacy of Piola,
Mindlin. Mathematics and Mechanics of Solids: Sedov and Toupin and some future research
perspectives.
dell’Isola, F., Giorgio, I., Pawlikowski, M., & Rizzi, N. (2016b). Large deformations of planar extensible beams and pantographic lattices: Heuristic homogenization, experimental and numerical
examples of equilibrium. Proceedings of The Royal Society A, 472(2185).
dell’Isola, F., Della Corte, A., Greco, L., & Luongo, A. (2016c). Plane bias extension test for
a continuum with two inextensible families of fibers: A variational treatment with Lagrange
multipliers and a perturbation solution. International Journal of Solids and Structures.