×

The effective mechanical properties of nonlinear isotropic composites. (English) Zbl 0734.73052

Summary: A new variational structure is proposed that yields a prescription for the effective energy potentials of nonlinear composites in terms of the corresponding energy potentials for linear composites with the same microstructural distributions. The prescription can be used to obtain bounds and estimates for the effective mechanical properties of nonlinear composites from any bounds and estimates that may be available for the effective properties of linear composites. The main advantages of the procedure are the simplicity of its implementation, the generality of its applications and the strength of its results. The general prescription is applied to three special nonlinear composites: a porous material, a two- phase incompressible composite and a rigidly reinforced material. The results are compared with previously available results for the special case of power-law constitutive behavior.

MSC:

74E30 Composite and mixture properties
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics

Citations:

Zbl 0734.73053
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Avellaneda, M., Commun. Pure appl. Math, 40, 527 (1987) · Zbl 0629.73010
[2] Boucher, S., J. Compos. Mater., 8, 82 (1974)
[3] Budiansky, B., J. Mech. Phys. Solids, 13, 223 (1965)
[4] Budiansky, B.; Hutchinson, J. W.; Slutsky, S., (Hopkins, H. G.; Sewell, M. J., Mechanics of Solids, The Rodney Hill 60th anniversary volume (1982), Pergamon Press: Pergamon Press Oxford), 539 · Zbl 0473.00012
[5] Christensen, R. M., Mechanics of Composite Materials, ((1979), Wiley Interscience: Wiley Interscience New York) · Zbl 0829.73061
[6] Duva, J. M., J. Engng Mater. Technol., 196, 317 (1984)
[7] Duva, J. M.; Hutchinson, J. W., Mech. Mater., 3, 41 (1984)
[8] Hashin, Z.; Shtrikman, S., J. Mech. Phys. Solids, 10, 335 (1962)
[9] Hill, R., J. Mech. Phys. Solids, 5, 66 (1956) · Zbl 0073.23703
[10] Hill, R., J. Mech. Phys. Solids, 11, 357 (1963) · Zbl 0114.15804
[11] Hill, R., J. Mech. Phys. Solids, 13, 213 (1965)
[12] Kohn, R. V., (Sih, G., Composite Material Response: Constitutive Relations and Damage Mechanisms (1988), Elsevier), 155
[13] Marcellini, P., Ann. Mater. Pura. Appl., 117, 139 (1978) · Zbl 0395.49007
[14] McLaughlin, R., Int. J. Engng Sci., 15, 237 (1977) · Zbl 0349.73050
[15] Milton, G. W., Some Exact Models in Statistical Physics, (Ph.D. Thesis (1985), Cornell University: Cornell University Ithaca)
[16] Muller, S., Archs ration Mech. Analysis, 99, 189 (1987) · Zbl 0629.73009
[17] Ponte Castañeda, P., (Proc. R. Soc. (Lond), A422 (1989)), 147 · Zbl 0673.73005
[18] Ponte Castañlda, P.; Ponte Castañlda, P.
[19] Ponte Castañlda, P.; Willis, J. R., (Proc. R. Soc. (Lond), A416 (1988)), 217 · Zbl 0635.73006
[20] Sanchez-Palencia, E., Lecture Notes in Physics 127, (Non-homogeneous Media and Vibration Theory (1980), Springer: Springer Heidelberg) · Zbl 0432.70002
[21] Talbot, D. R.S.; Willis, J. R., IMA J. appl. Math., 35, 39 (1985) · Zbl 0588.73025
[22] Van Tiel, J., Convex Analysis, ((1984), Wiley: Wiley New York) · Zbl 0453.26002
[23] Willis, J. R., (Hopkins, H. G.; Sewell, M. J., Mechanics of Solids. The Rodney Hill 60th anniversary volume (1982), Pergamon Press: Pergamon Press Oxford), 653 · Zbl 0473.00012
[24] Willis, J. R., J. appl Mech., 50, 1202 (1983) · Zbl 0539.73003
[25] Willis, J. R., (Weng, G. J.; Taya, M.; Abe, H., Micromechanics and Inhomogeneity, the Toshio Mura anniversary volume (1989), Springer: Springer New York), 581
[26] Willis, J. R., IMA J. appl. Math., 43, 231 (1990)
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.