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


74A20 Theory of constitutive functions in solid mechanics
76S05 Flows 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.
[6] Flynn, C. P.: Point defects and diffusion. Oxford: Clarendon Press. 1972. · Zbl 0356.54016
[7] Aravin, V. I., Numerov, S. N.: Theory of fluid flow in undeformable porous media. (Translated from Russian.) New York: Daniel Davey & Co. 1965.
[8] Scheidegger, A. E.: The physics of flow through porous media. Toronto: University of Toronto Press. 1974. · Zbl 0082.40402
[9] Atkin, R. J., Craine, R. E.: Continuum theories of mixtures: Basic theory and historical development. Quart. J. Mech. Appl. Math.29, 209-244 (1976). · Zbl 0339.76003 · doi:10.1093/qjmam/29.2.209
[10] Atkin, R. J., Craine, R. E.: Continuum theories of mixtures: Applications. J. Inst. Math. Appl.17, 153-207 (1976). · Zbl 0355.76004 · doi:10.1093/imamat/17.2.153
[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
[13] Truesdell, C.: Mechanical basis for diffusion. J. Chem. Phys.37, 2336-2344 (1962). · doi:10.1063/1.1733007
[14] Aifantis, E. C.: Diffusion of a perfect fluid in a linear elastic stress field. Mech. Res. Comm.3, 245-250 (1976). · Zbl 0366.76070 · doi:10.1016/0093-6413(76)90053-7
[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
[20] Cattaneo, C.: Atti del Seminario Matematico e Fisico della Universita di Modena3, 3-21 (1948).
[21] 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). · Zbl 1339.35135
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.