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Generalized self-consistent homogenization using the finite element method. (English) Zbl 1160.74038

Summary: This paper presents a development of the usual generalized self-consistent method for homogenization of composite materials. The classical self-consistent scheme is appropriate for phases that are “disordered”, i.e. what is called “random texture”. In the case of both linear and nonlinear components, the self-consistent homogenization can be used to identify expressions for bounds on effective mechanical characteristics. In this paper we formulate a coupled thermo-mechanical problem for nonlinear composites having properties depending on temperature. The solution is found in a non-classical way, as we use the finite element method to solve the elastic-plastic problem at hand. In this sense we propose a “problem-oriented” technique of solution. The method is finally applied to the real case of superconducting strands used for the coils of the future ITER experimental reactor.

MSC:

74Q05 Homogenization in equilibrium problems of solid mechanics
74E30 Composite and mixture properties
74S05 Finite element methods applied to problems in solid mechanics
74Q20 Bounds on effective properties in solid mechanics
74F05 Thermal effects in solid mechanics

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[1] A. Bensoussan, J.L. Lions, and G. Papanicolau, Asymptotic Analysis for Periodic Structures (North-Holland, Amsterdam, 1976).
[2] E. Sanchez-Palencia, Non-Homogeneous Media and Vibration Theory (Springer Verlag, Berlin, 1980). · Zbl 0432.70002
[3] Suquet, C.R. Acad. Sci. II (France) 295 pp 1355– (1983)
[4] P. Suquet, Element of Homogemization for Inelastic Solid Mechanics, in: Homogenization Techniques for Composite Media, Lecture Notes in Physics 272, edited by E. Sanchez-Palencia and A. Zaoui (Springer, New York, 1985) pp. 193-278.
[5] G.A. Francfort, Homogenisation and Fast Oscillations in Linear Thermoelasticity, in: Numerical Methods for Transient and Coupled Problems, edited by R. Lewis, E. Hinton, P. Betess and B. Schrefler (Pineridge Press, Swansea, 1984) pp. 382-392.
[6] Boutin, Int. J. Heat Mass Transf. 38(17) pp 3181– (1995)
[7] Boso, Cryogenics 46(7-8) pp 569– (2006)
[8] Boso, Cryogenics 45 pp 4– (2005)
[9] Hershey, Trans. ASME J. Appl. Mech. 21 pp 236– (1954)
[10] Hill, J. Mech. Phys. Solids 13 pp 213– (1965)
[11] Budiansky, J. Mech. Phys. Solids 13 pp 223– (1965)
[12] J. Aboudi, Mechanics of Composite Materials - A Unified Micromechanical Approach (Elsevier, Amsterdam, 1992). · Zbl 0837.73003
[13] Christensen, J. Mech. Phys. Solids 38(3) pp 379– (1990)
[14] Hashin, J. Compos. Mater. 2 pp 284– (1968)
[15] Miehe, Comput. Methods Appl. Mech. Eng. 171 pp 317– (1999)
[16] Pellegrino, Int. J. Numer. Methods Eng. 46 pp 1609– (1999)
[17] Boso, Methods Eng. 16(9) pp 615– (2000)
[18] Hain, Comput. Mech. 42 pp 197– (2008)
[19] Simo, Int. J. Numer. Methods Eng. 22(3) pp 649– (1986)
[20] J.C. Simo and T.J.R. Hughes, Computational inelasticity (Springer-Verlag, New York, 1998). · Zbl 0934.74003
[21] Hervé, Int. J. Eng. Sci. 33(10) pp 1419– (1995)
[22] O.C. Zienkiewicz and R.L. Taylor, The Finite Element Method for Solid and Structural Mechanics (Elsevier, Butterworth-Hein, 2005). · Zbl 1084.74001
[23] Gibiansky, J. Mech. Phys. Solids 48 pp 461– (2000)
[24] P. Bauer, H. Rajainmaki, and E. Salpietro, EFDA Material Data Compilation for Superconductor Simulation, EFDA CSU, Garching, April 07, unpublished.
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