Mathematical Modelling of Diffusive and Mechanical Processes in Bodies with Microstructure
Burak Yaroslav 1, Chaplya Yevhen 1,2, Chernukha Olha 1, Owedyk Jan 2,3
1Centre of Mathematical Modelling of Pidstryhach Institute of Applied Problems of Mechanics and Mathematics
The Ukrainian National Academy of Sciences
Dudayev Str. 15, 79005 Lviv, Ukraine
e-mail: {burak/chaplia/cher}@cmm.lviv.ua
2Kazimierz Wielki University in Bydgoszcz
ul. Chodkiewicza 30, 85-064 Bydgoszcz, Poland
e-mail:{czapla/jowedyk}@ukw.edu.pl
3The Division of Applied Computer Science, Academy of Humanities and Economics in Łódź
ul. Wojska Polskiego 46A, 85-825 Bydgoszcz, Poland
e-mail: jowedyk@wshe.lodz.pl
Received:
Received: 14 May 2008; published online: 8 December 2008
DOI: 10.12921/cmst.2008.14.02.87-95
OAI: oai:lib.psnc.pl:652
Abstract:
The continuum-thermodynamical approach is proposed for describing mechanical and diffusive processes in bodies with microstructure. Different physical states of admixture particles in a local body structure are taken into account. Features of a stresseddeformable state are discussed on an example of diffusive saturation of a layer in this case.
Key words:
diffusion and mechanics, microstructure, thermodynamical model
References:
[1] Physical metallurgy, Ed. E. W. Cahn, Amsterdam, North-Holland Pub. Com, 1965.
[2] T. I. Kucher, Diffusion from vapour phase into a crystal with account two possible diffusion mechanisms and exchange between them. Physics of Solid State 6(3), 801-810 (1964).
[3] E. C. Aifantis, Continuum basis for diffusion in regions with multiple diffusivity. J. Appl. Phys. 50(3), 1334-1338 (1979).
[4] E. C. Aifantis and J. M. Hill, On the theory of diffusion in media with double diffusivity. I. Basic mathematical results. Q. J. Mech. Math. 33(1), 1-21 (1980).
[5] E. C. Aifantis, A new interpretation of diffusion in highdiffusivity paths – a continuum approach. Acta Met. 27, 683-691 (1982).
[6] Ya. I. Burak, B. P. Galapats and Ye. Ya. Chaplya, Deformation of electrically conducting solids taking into consideration heterodiffusion of charged impurity particles. J. Materials Science 16(5) 395-400 (1981).
[7] Ya. I. Burak, B. P. Galapats and Ye. Ya. Chaplya, Basic equations for process of deformation of electrically conducting solid solutions with account distinct admixture diffusion ways. Mathematical Methods and Physicomechanical Fields 11, 60-66 (1980).
[8] A. C. Eringen, Mechanics of Continuum, New York: John Wiley and Sons (1967).
[9] S. R. De Groot and P. Mazur, Non-equilibrium Thermodynamics, New York: Dover Publications, 1984.
[10] Y. Y. Burak, Y. Y. Chaplya and O. Y. Chernukha, Continual-thermodynamical models of solid solution mechanics, Kyiv: Naukova Dumka (2006).
[11] I. Gyarmati, Non-equilibrium Thermodynamics, New York: Springer-Verlag (1970).
[12] I. Prigogine, Introduction to Thermodynamics of Irreversible Processes, Illinois: Sprinfild (1955).
[13] J. W.Gibbs, The Collected Works of J. W. Gibbs, v. 1, New Haven: Yale University Press (1948).
[14] Y. S. Podstrihach and R. N. Shvets, Thermoelastisity of thin shells, Kyiv: Naukova Dumka (1978).
The continuum-thermodynamical approach is proposed for describing mechanical and diffusive processes in bodies with microstructure. Different physical states of admixture particles in a local body structure are taken into account. Features of a stresseddeformable state are discussed on an example of diffusive saturation of a layer in this case.
Key words:
diffusion and mechanics, microstructure, thermodynamical model
References:
[1] Physical metallurgy, Ed. E. W. Cahn, Amsterdam, North-Holland Pub. Com, 1965.
[2] T. I. Kucher, Diffusion from vapour phase into a crystal with account two possible diffusion mechanisms and exchange between them. Physics of Solid State 6(3), 801-810 (1964).
[3] E. C. Aifantis, Continuum basis for diffusion in regions with multiple diffusivity. J. Appl. Phys. 50(3), 1334-1338 (1979).
[4] E. C. Aifantis and J. M. Hill, On the theory of diffusion in media with double diffusivity. I. Basic mathematical results. Q. J. Mech. Math. 33(1), 1-21 (1980).
[5] E. C. Aifantis, A new interpretation of diffusion in highdiffusivity paths – a continuum approach. Acta Met. 27, 683-691 (1982).
[6] Ya. I. Burak, B. P. Galapats and Ye. Ya. Chaplya, Deformation of electrically conducting solids taking into consideration heterodiffusion of charged impurity particles. J. Materials Science 16(5) 395-400 (1981).
[7] Ya. I. Burak, B. P. Galapats and Ye. Ya. Chaplya, Basic equations for process of deformation of electrically conducting solid solutions with account distinct admixture diffusion ways. Mathematical Methods and Physicomechanical Fields 11, 60-66 (1980).
[8] A. C. Eringen, Mechanics of Continuum, New York: John Wiley and Sons (1967).
[9] S. R. De Groot and P. Mazur, Non-equilibrium Thermodynamics, New York: Dover Publications, 1984.
[10] Y. Y. Burak, Y. Y. Chaplya and O. Y. Chernukha, Continual-thermodynamical models of solid solution mechanics, Kyiv: Naukova Dumka (2006).
[11] I. Gyarmati, Non-equilibrium Thermodynamics, New York: Springer-Verlag (1970).
[12] I. Prigogine, Introduction to Thermodynamics of Irreversible Processes, Illinois: Sprinfild (1955).
[13] J. W.Gibbs, The Collected Works of J. W. Gibbs, v. 1, New Haven: Yale University Press (1948).
[14] Y. S. Podstrihach and R. N. Shvets, Thermoelastisity of thin shells, Kyiv: Naukova Dumka (1978).
