Micro1
Subject Areas : Smart & Advanced Materials
1 - دانشکده فنی تهران جنوب
Keywords: micropolar, thermoelasticity, FGM,
Abstract :
The origin of the modern theories of a continuum with microstructure goes back to papers by Ericksen and Truesdell (1958), Mindlin (1964), Eringen and Suhubi (1964) and Green and Rivlin (1964). Green (1965) has established the connection of the theory of multipolar continuum mechanics and the other theories. Much of the theoretical progress in the field is discussed in the books of Kunin (1983), Ciarletta and Iesan (1993) and Eringen (1999). In the theory of micromorphic bodies formulated by Eringen and Suhubi (1964, 1999) the material particle is endowed with three deformable directors and the theory introduces nine extra degrees of freedom over the classical theory. On the basis of the theory of bodies with inner structure, Grot (1969) has established a theory of thermodynamics of elastic bodies with microstructure whose microelements possess microtemperatures. The Clausius–Duhem inequality is modified to include microtemperatures, and the firstorder moment of the energy equations are added to the usual balance laws of a continuum with microstructure. The theory of micromorphic fluids with microtemperatures has been studied in various papers (see, e.g., Koh, 1973; Riha, 1975, 1977; Verma et al., 1979). Riha (1976) has presented a study of heat conduction in materials with microtemperatures. Experimental data for the silicone rubber containing spherical aluminium particles and for human blood were found to conform closely to predicted theoretical thermal conductivity.
Casas, P., Quintanilla, R., 2005. Exponential stability in thermoelasticity with microtemperatures. Int. J. Eng. Sci. 43, 33–47.
Ciarletta, M., Iesan, D., 1993. Non-Classical Elastic Solids. Longman Scientific & Technical, London.
Ericksen, J., Truesdell, C., 1958. Exact theory of stress and strain in rods and shells. Arch. Ration. Mech. Anal. 1, 295–323.
Eringen, A.C., 1999. Microcontinuum Field Theories, I. Foundations and Solids. Springer-Verlag, New York, Berlin, Heidelberg.
Eringen, A.C., Suhubi, E.S., 1964. Nonlinear theory of simple microelastic solids. Int. J. Eng. Sci. 2, 389–403.
Green, A.E., 1965. Micro-materials and multipolar continuum mechanics. Int. J. Eng. Sci. 3, 533–537.
Green, A.E., Rivlin, R.S., 1964. Multipolar continuum mechanics. Arch. Ration. Mech. Anal. 17, 113–147.
Grot, R., 1969. Thermodynamics of a continuum with microstructure. Int. J. Eng. Sci. 7, 801–814.
Iesan, D., 2001. On a theory of micromorphic elastic solids with microtemperatures. J. Thermal Stresses 24, 737–752.
Iesan, D., 2004. Thermoelastic Models of Continua. Kluwer Academic Publishers, Dordrecht.
Koh, S.L., 1973. Theory of a second-order microfluid. Rheol. Acta 12, 418–430.
Kunin, I.A., 1983. Elastic Media with Microstructure. Springer-Verlag, Berlin.
Mindlin, R.D., 1964. Microstructure in linear elasticity. Arch. Ration. Mech. Anal. 16, 51–77.
Riha, P., 1975. On the theory of heat-conducting micropolar fluids with microtemperatures. Acta Mech. 23, 1–8.
Riha, P., 1976. On the microcontinuum model of heat conduction in materials with inner structure. Int. J. Eng. Sci. 14, 529–535.
Riha, P., 1977. Poiseuille flow of microthermopolar fluids. Acta Tech. CSAV 22, 602–614.
Scalia, A., Svanadze, M., 2006. On the representation of solutions of the theory of thermoelasticity with microtemperatures. J. Thermal
Stresses 29, 849–863.
Svanadze, M., 2003. Boundary value problems of the theory of thermoelasticity with microtemperatures. Proc. GAMM, PAMM 3, 188–
189.
Svanadze, M., 2004. Fundamental solutions of the equations of the theory of thermoelasticity with microtemperatures. J. Thermal Stresses
27, 151–170.
Verma, P.D.S., Singh, D.V., Singh, K., 1979. Hagen–Poiseuille flow of microthermopolar fluids in a circular pipe. Acta Tech. CSAV 24,
402–412.