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Keywords:
extended Hashin-Shtrikman variational principle; eigenparameter; transformation field analysis
extended Hashin-Shtrikman variational principle; eigenparameter; transformation field analysis
Summary:
Internal parameters, eigenstrains, or eigenstresses, arise in functionally graded materials, which are typically present in particulate, layered, or rock bodies. These parameters may be realized in different ways, e.g., by prestressing, temperature changes, effects of wetting, swelling, they may also represent inelastic strains, etc. In order to clarify the use of eigenparameters (eigenstrains or eigenstresses) in physical description, the classical formulation of elasticity is presented, and the two most important Lagrange’s and Castigliano’s variational principles are formulated in the sequel. Then the classical Hashin-Shtrikman principles are recalled and the involvement of eigenparameters is studied in more detail.
References:
[1] Z. Bittnar, J. Šejnoha: Numerical methods in structural mechanics. ASCE Press, New York, Thomas Telford, co-publisher, London, 1996.
[2] G. J. Dvorak: Transformation field analysis of inelastic composite materials. Proc. Roy. Soc. London. Ser. A 437 (1992), 311–327. DOI 10.1098/rspa.1992.0063 | MR 1163551 | Zbl 0748.73007
[3] G. J. Dvorak, P. Procházka: Thick-walled composite cylinders with optimal fiber prestress. Composites, Part B 27B (1996), 643–649. DOI 10.1016/S1359-8368(96)00001-7
[4] G. J. Dvorak, P. Procházka, and M. V. Srinivas: Design and fabrication of submerged cylindrical laminates. Internat. J. Solids Structures 36 (1999), 3917–3943. DOI 10.1016/S0020-7683(98)00181-4 | MR 1737571
[5] W. J. Drugan, J. R. Willis: A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites. J. Mech. Phys. Solids 44 (1996), 497–524. DOI 10.1016/0022-5096(96)00007-5 | MR 1381396
[6] J. D. Eshelby: The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. Roy. Soc. London, Ser. A 241 (1957), 376–396. DOI 10.1098/rspa.1957.0133 | MR 0087326 | Zbl 0079.39606
[7] Z. Hashin, S. Shtrikman: On some variational principles in anisotropic and nonhomogeneous elasticity. J. Mech. Phys. Solids 10 (1962), 335–342. DOI 10.1016/0022-5096(62)90004-2 | MR 0147031
[8] Z. Hashin, S. Shtrikman: A variational approach to the theory of the elastic behaviour of polycristals. J. Mech. Phys. Solids 10 (1962), 343–352. DOI 10.1016/0022-5096(62)90005-4 | MR 0147032
[9] Z. Hashin: Extremum principles for elastic heterogeneous media with imperfect interfaces and their application to bounding of effective moduli. J. Mech. Phys. Solids 40 (1992), 767–781. DOI 10.1016/0022-5096(92)90003-K | MR 1163486 | Zbl 0760.73077
[10] R. Hill: New derivation of some elastic extremum principles. Progress in Applied Mechanics. The Prager Anniversary Volume, New York (1963), 99–106. MR 0160359
[11] I. M. Levin: Determination of composite material elastic and thermoelastic constants. Izv. AN SSSR, Mekhanika Tverdogo Tela 11 (1976), 137–145. (Russian)
[12] P. Ponte Castañeda: The effective mechanical properties of nonlinear isotropic composites. J. Mech. Phys. Solids 39 (1991), 45–71. DOI 10.1016/0022-5096(91)90030-R | MR 1085622
[13] P. Procházka: Optimal eigenstress fields in layered structures. J. Comput. Appl. Math. 63 (1995), 475–480. DOI 10.1016/0377-0427(95)00093-3 | MR 1365583
[14] P. Procházka, J. Šejnoha: Behavior of composites on bounded domain. BE Communications 7 (1996), 6–8.
[15] M. V. Srinivas, G. J. Dvorak, and P. Procházka: Design and fabrication of submerged cylindrical laminates. II: Effect of fiber pre-stress. Internat. J. Solids Structures 36 (1999), 3943–3976. DOI 10.1016/S0020-7683(98)00182-6
[16] J. R. Willis: Bounds and self-consistent estimates for the overall properties of anisotropic composites. J. Mech. Phys. Solids 25 (1977), 185–202. DOI 10.1016/0022-5096(77)90022-9 | Zbl 0363.73014
[17] J. R. Willis: On methods for bounding the overall properties of nonlinear composites. J. Mech. Phys. Solids 39 (1991), 73–86. DOI 10.1016/0022-5096(91)90031-I | MR 1085623 | Zbl 0734.73053
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