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On the problem of diffusion in solids. (English) Zbl 0447.73002

74A20Theory of constitutive functions
76S05Flows in porous media; filtration; seepage
Full Text: DOI
[1] Fick, A.: Über Diffusion. Pogg. Ann. Phys. Chem.94, 58-86 (1855).
[2] Darcy, H.: Les fontaines publiques de la ville de dijon. Paris: Dalmont. 1856.
[3] Shewmon, P. G.: Diffusion in solids. New York: McGraw-Hill. 1963.
[4] Adda, Y., Phillibert, J.: La diffusion dans les solides, Tomes I & II. Paris: Presses Universitaires de France. 1966.
[5] Girifalco, L. A., Welch, D. O.: Point defects and diffusion in strained metals. New York: Gordon & Breach. 1967.
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[11] Bowen, R. M.: Theory of mixtures, in: Continuum physics III (Eringen, A. C., ed.). New York: Academic Press. 1976.
[12] Truesdell, C.: Sulle Basi della termomeccanica. Rend. Lincei (8)22, 33-38 158 to 166 (1957). · Zbl 0098.21002
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[15] Aifantis, E. C., Gerberich, W. W.: Gaseous diffusion in a stressed thermoelastic solid ? I: The thermomechanical formulation. Acta Mech.28, 1-24 (1977). · Zbl 0391.76069 · doi:10.1007/BF01208785
[16] 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). · Zbl 0404.76077 · doi:10.1007/BF01208786
[17] Aifantis, E. C.: Introducing a multi-porous medium. Developments in mechanics8, 209-211 (1977).
[18] 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). · Zbl 0104.21702
[19] Spencer, A. J. M.: Theory of invariants, in: Continuum physics I (Eringen, A. C., ed.). New York: Academic Press. 1971. · Zbl 0209.55201
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[22] Maxwell, J. C.: On the dynamical theory of gases. Phil. Trans. Roy. Soc. (Lond.)157, 49-88 (1867). · doi:10.1098/rstl.1867.0004
[23] 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.) · Zbl 0136.46703
[24] Ting, T. W.: Certain non-steady flows of second-order fluids. Arch. Rat. Mech. Anal.14, 1-26 (1963). · Zbl 0139.20105 · doi:10.1007/BF00250690
[25] Chen, P. J., Gurtin, M. E.: On a theory of heat conduction involving two temperatures. ZAMP19, 614-627 (1968). · Zbl 0159.15103 · doi:10.1007/BF01594969
[26] Ting, T. W.: Parabolic and pseudoparabolic partial differential equations. J. Math. Soc. Japan21, 440-453 (1969). · Zbl 0177.36701 · doi:10.2969/jmsj/02130440
[27] Ting, T. W.: A cooling process according to two-temperature theory of heat conduction. J. Math. Anal. Appl.45, 23-31 (1974). · Zbl 0272.35039 · doi:10.1016/0022-247X(74)90116-4
[28] Volterra, V.: Theory of functionals and of integral and integro differential equations. New York: Dover Publications. 1959. · Zbl 0086.10402
[29] Gurtin, M. E., Pipkin, A. C.: A general theory of heat conduction with finite wave speeds. Arch. Rat. Mech. Anal.31, 113-126 (1968). · Zbl 0164.12901 · doi:10.1007/BF00281373
[30] Van Leeuwen, H. P.: A quantitative model of hydrogen induced grain boundary cracking. J. Corros., NACE29, 197-204 (1973).
[31] Nowacki, W.: Certain problems of thermo-diffusion in solids. Arch. Mech.23, 731-755 (1971). · Zbl 0264.73006
[32] 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.
[33] Suklje, L.: Rheological aspects of soil mechanics. London: Wiley-Interscience. 1969.
[34] Bear, J.: Dynamics of fluids in porous media. New York: Elsevier. 1972. · Zbl 1191.76001
[35] Aifantis, E. C.: A new interpretation of diffusion in regions with high-diffusivity paths. A continuum approach. Acta Metallurgica27, 683-691 (1979). · doi:10.1016/0001-6160(79)90019-1
[36] Aifantis, E. C.: Continuum basis for diffusion in regions with multiple diffusivity. J. Appl. Phys.50, 1334-1338 (1979). · doi:10.1063/1.326167