References
Artstein, Z., Look for the Extreme Points, SIAM Review 22, 1980, 172–185.
Avellaneda, M., Optimal Bounds and Microgeometries for Elastic Two-phase Composites, SIAM J. Appl. Math. 47, 1987, 1216–1228.
Allaire, G. & Kohn, R. V., Optimal Bounds on the Effective Behaviour of a Mixture of Two Well Ordered Elastic Materials, Quart. Appl. Math. 51, 1993, 643–674.
Avellaneda, M. & Milton, G. W., Bounds on the Effective Elasticity Tensor of Composites Based on Two Point Correlations, in Proceedings of the ASME Energy Technology Conference and Exposition, Houston, 1989, eds. Hui, D. & Kozic, T., ASME Press, New York, 1989.
Choi, M. D. & Lam, T. Y., An Old Question of Hubert, Queens Papers on Pure and Applied Math., Queens University, Kingston, Ontario, 1977.
Crouzeix, M. & Mignot, A. L., Analyse numérique des équations différentielles, Masson, Paris, 1984.
Dal Maso, G. & Kohn, R. V., The Local Character of G-closure, to appear.
Francfort, G. A. & Marigo, J. J., Stable Damage Evolution in a Brittle Continuous Medium, Eur. J. Mech. A./Solids 12, 1993, 149–189.
Francfort, G. A. & Murat, F., Homogenization and Optimal Bounds in Linear Elasticity, Arch. Rational Mech. Anal. 94, 1986, 307–334.
Hashin, Z., Analysis of Composite Materials, a Survey, J. Appl. Mech., Trans. ASME 105, 1983, 481–505.
Hilbert, D., Über die Darstellung definiter Formen als Summe von Formenquadraten, Math. Ann. 32, 1888, 342–350.
Hashin, Z., & Shtrikman, S., A Variational Approach to the Theory of the Elastic Behaviour of Multiphase Materials, J. Mech. Phys. Solids 11, 1963, 127–140.
Lipton, R., On the Behaviour of Elastic Composites with Transverse Isotropy Symmetry, J. Mech. Phys. Solids 39, 1991, 663–681.
Milton, G. W., On Characterizing the Set of Possible Effective Tensors of Composites: The Variational Method and the Translation Method, Comm. Pure Appl. Math. 43, 1990, 63–125.
Motzkin, T. S., The Arithmetic-Geometric Inequality, in Inequalities, ed. Shisha, O., Academic Press, New York, 1967, 205–224.
Milton, G. W. & Kohn, R. V., Variational Bounds on the Effective Moduli of Anisotropic Composites, J. Mech. Phys. Solids 36, 1988, 597–629.
Murat, F. & Tartar, L., H-convergence, in Topics in the Mathematical Modelling of Composite Materials, ed. R. V. Kohn, Birkhaüser, Boston, to appear.
Tartar L., Cours Peccot, 1977, Collège de France, Paris; partially written in [MT].
Author information
Authors and Affiliations
Additional information
Communicated by J. Ball
Rights and permissions
About this article
Cite this article
Francfort, G., Murat, F. & Tartar, L. Fourth-order moments of nonnegative measures on S2 and applications. Arch. Rational Mech. Anal. 131, 305–333 (1995). https://doi.org/10.1007/BF00380913
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00380913