On the problem of diffusion in solids

Elias C. Aifantis1
1216 Talbot Laboratory, University of Illinois at Urbana-Champaign, Urbana, USA

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Tài liệu tham khảo

Fick, A.: Über Diffusion. Pogg. Ann. Phys. Chem.94, 58?86 (1855).

Darcy, H.: Les fontaines publiques de la ville de dijon. Paris: Dalmont. 1856.

Shewmon, P. G.: Diffusion in solids. New York: McGraw-Hill. 1963.

Adda, Y., Phillibert, J.: La diffusion dans les solides, Tomes I & II. Paris: Presses Universitaires de France. 1966.

Girifalco, L. A., Welch, D. O.: Point defects and diffusion in strained metals. New York: Gordon & Breach. 1967.

Flynn, C. P.: Point defects and diffusion. Oxford: Clarendon Press. 1972.

Aravin, V. I., Numerov, S. N.: Theory of fluid flow in undeformable porous media. (Translated from Russian.) New York: Daniel Davey & Co. 1965.

Scheidegger, A. E.: The physics of flow through porous media. Toronto: University of Toronto Press. 1974.

Atkin, R. J., Craine, R. E.: Continuum theories of mixtures: Basic theory and historical development. Quart. J. Mech. Appl. Math.29, 209?244 (1976).

Atkin, R. J., Craine, R. E.: Continuum theories of mixtures: Applications. J. Inst. Math. Appl.17, 153?207 (1976).

Bowen, R. M.: Theory of mixtures, in: Continuum physics III (Eringen, A. C., ed.). New York: Academic Press. 1976.

Truesdell, C.: Sulle Basi della termomeccanica. Rend. Lincei (8)22, 33?38 158 to 166 (1957).

Truesdell, C.: Mechanical basis for diffusion. J. Chem. Phys.37, 2336?2344 (1962).

Aifantis, E. C.: Diffusion of a perfect fluid in a linear elastic stress field. Mech. Res. Comm.3, 245?250 (1976).

Aifantis, E. C., Gerberich, W. W.: Gaseous diffusion in a stressed thermoelastic solid ? I: The thermomechanical formulation. Acta Mech.28, 1?24 (1977).

Aifantis, E. C., Gerberich, W. W.: Gaseous diffusion in a stressed thermoelastic solid ? II: Thermodynamic structure and transport theory. Acta Mech.28, 25?47 (1977).

Aifantis, E. C.: Introducing a multi-porous medium. Developments in mechanics8, 209?211 (1977).

Barenblatt, G. I., Zheltov, Iu. P., Kochina, I. N.: Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks (strata). PMM24, 1286?1303 (1960). (Transl. of Priklad. Mat. Mekh.24, 852?864).

Spencer, A. J. M.: Theory of invariants, in: Continuum physics I (Eringen, A. C., ed.). New York: Academic Press. 1971.

Cattaneo, C.: Atti del Seminario Matematico e Fisico della Universita di Modena3, 3?21 (1948).

Cattaneo, C.: Sur une forme de l'équation de la chaleur éliminant le paradoxe d'une propagation instantanée. Compt. Rend. Acad. Sci.247, 431?433 (1958).

Maxwell, J. C.: On the dynamical theory of gases. Phil. Trans. Roy. Soc. (Lond.)157, 49?88 (1867).

Barenblatt, G. I.: On certain boundary-value problems for the equations of seepage of a liquid in fissured rocks. PMM27, 513?518 (1963). (Transl. of Priklad. Mat. Mekh.27, 784?793.)

Ting, T. W.: Certain non-steady flows of second-order fluids. Arch. Rat. Mech. Anal.14, 1?26 (1963).

Chen, P. J., Gurtin, M. E.: On a theory of heat conduction involving two temperatures. ZAMP19, 614?627 (1968).

Ting, T. W.: Parabolic and pseudoparabolic partial differential equations. J. Math. Soc. Japan21, 440?453 (1969).

Ting, T. W.: A cooling process according to two-temperature theory of heat conduction. J. Math. Anal. Appl.45, 23?31 (1974).

Volterra, V.: Theory of functionals and of integral and integro differential equations. New York: Dover Publications. 1959.

Gurtin, M. E., Pipkin, A. C.: A general theory of heat conduction with finite wave speeds. Arch. Rat. Mech. Anal.31, 113?126 (1968).

Van Leeuwen, H. P.: A quantitative model of hydrogen induced grain boundary cracking. J. Corros., NACE29, 197?204 (1973).

Nowacki, W.: Certain problems of thermo-diffusion in solids. Arch. Mech.23, 731?755 (1971).

Gurtin, M. E.: On the linear theory of diffusion through an elastic solid. Proc. Conf. Environmental Degradation Engng. Matl's. pp. 107?119, Blacksburg, 1977.

Suklje, L.: Rheological aspects of soil mechanics. London: Wiley-Interscience. 1969.

Bear, J.: Dynamics of fluids in porous media. New York: Elsevier. 1972.

Aifantis, E. C.: A new interpretation of diffusion in regions with high-diffusivity paths. A continuum approach. Acta Metallurgica27, 683?691 (1979).

Aifantis, E. C.: Continuum basis for diffusion in regions with multiple diffusivity. J. Appl. Phys.50, 1334?1338 (1979).