Algebra, Geometry, and Computations of Exact Relations for Effective Moduli of Composites

[1]  V. B. Levenshtam.  Higher-Order Approximations of the Averaging Method for Parabolic Initial-Boundary Value Problems with Rapidly Oscillating Coefficients , 2003 .

[2]  G. Milton.  The Theory of Composites , 2002 .

[3]  U. Raitums.  On the Local Representation of G-Closure , 2001 .

[4]  W. Drugan.  Micromechanics-based variational estimates for a higher-order nonlocal constitutive equation and optimal choice of effective moduli for elastic composites , 2000 .

[5]  Daniel S. Sage,et al.  Exact relations for effective tensors of composites: Necessary conditions and sufficient conditions , 2000 .

[6]  Robert V. Kohn,et al.  Topics in the Mathematical Modelling of Composite Materials , 1997 .

[7]  David M. Raup,et al.  How Nature Works: The Science of Self-Organized Criticality , 1997 .

[8]  W. Drugan,et al.  A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites , 1996 .

[9]  I. Ruzin,et al.  Theory of the fractional quantum Hall effect: The two-phase model. , 1994, Physical review. B, Condensed matter.

[10]  G. Francfort,et al.  Sets of conductivity and elasticity tensors stable under lamination , 1994 .

[11]  S. P. Neuman,et al.  Prediction of steady state flow in nonuniform geologic media by conditional moments: Exact nonlocal , 1993 .

[12]  Antoine Saucier,et al.  Effective permeability of multifractal porous media , 1992 .

[13]  V. Zhikov,et al.  Estimates for the averaged matrix and the averaged tensor , 1991 .

[14]  P. King.  The use of renormalization for calculating effective permeability , 1989 .

[15]  Milton.  Classical Hall effect in two-dimensional composites: A characterization of the set of realizable effective conductivity tensors. , 1988, Physical review. B, Condensed matter.

[16]  Robert V. Kohn,et al.  Optimal bounds for the effective energy of a mixture of isotropic, incompressible, elastic materials , 1988 .

[17]  Tang,et al.  Self-organized criticality. , 1988, Physical review. A, General physics.

[18]  Gilles A. Francfort,et al.  Homogenization and optimal bounds in linear elasticity , 1986 .

[19]  G. Marsily.  Quantitative Hydrogeology: Groundwater Hydrology for Engineers , 1986 .

[20]  D. Stroud,et al.  New exact results for the Hall coefficient and magnetoresistance of inhomogeneous two-dimensional metals , 1984 .

[21]  Andrej Cherkaev,et al.  G-closure of some particular sets of admissible material characteristics for the problem of bending of thin elastic plates , 1984 .

[22]  Andrej Cherkaev,et al.  On the existence of solutions to some problems of optimal design for bars and plates , 1984 .

[23]  George Papanicolaou,et al.  Bounds for effective parameters of heterogeneous media by analytic continuation , 1983 .

[24]  S. Childress,et al.  Macroscopic Properties of Disordered Media , 1982 .

[25]  A. Bensoussan,et al.  Asymptotic analysis for periodic structures , 1979 .

[26]  K. Mendelson,et al.  A theorem on the effective conductivity of a two‐dimensional heterogeneous medium , 1975 .

[27]  Rodney Hill,et al.  Theory of mechanical properties of fibre-strengthened materials—III. self-consistent model , 1965 .

[28]  Rodney Hill,et al.  Theory of mechanical properties of fibre-strengthened materials: I. Elastic behaviour , 1964 .

[29]  Joseph B. Keller,et al.  A Theorem on the Conductivity of a Composite Medium , 1964 .

[30]  R. Hill.  Elastic properties of reinforced solids: some theoretical principles , 1963 .

[31]  G. Backus.  Long-Wave Elastic Anisotropy Produced by Horizontal Layering , 1962 .

[32]  Chandler Davis.  All convex invariant functions of hermitian matrices , 1957 .

[33]  G. Milton,et al.  Rank one plus a null-Lagrangian is an inherited property of two-dimensional compliance tensors under homogenisation , 1998, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[34]  D. Turcotte.  Self-organized criticality , 1999 .

[35]  Per Bak,et al.  How Nature Works , 1996 .

[36]  V. Zhikov,et al.  Homogenization of Differential Operators and Integral Functionals , 1994 .

[37]  Y. Grabovsky.  The G-closure of two well-ordered, anisotropic conductors , 1993, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[38]  Graeme W. Milton,et al.  On characterizing the set of possible effective tensors of composites: The variational method and the translation method , 1990 .

[39]  G. Francfort,et al.  Optimal bounds for conduction in two-dimensional, multiphase, polycrystalline media , 1987 .

[40]  K. Lurie,et al.  Exact estimates of the conductivity of a binary mixture of isotropic materials , 1986, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[41]  R. Figari,et al.  An approach through orthogonal projections to the study of in homogeneous or random media with linear response , 1986 .

[42]  Andrej Cherkaev,et al.  Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion , 1984, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[43]  D. Bergman,et al.  Improved rigorous bounds on the effective elastic moduli of a composite material , 1984 .

[44]  W. Kohler,et al.  Bounds for the effective conductivity of random media , 1982 .

[45]  J. Willis.  Elasticity Theory of Composites , 1982 .

[46]  L. Tartar,et al.  Estimation de Coefficients Homogenises , 1979 .

[47]  E. Giorgi,et al.  Sulla convergenza degli integrali dell''energia per operatori ellittici del secondo ordine , 1973 .

[48]  A. Dykhne.  Conductivity of a Two-dimensional Two-phase System , 1971 .

[49]  S. Spagnolo,et al.  Sulla convergenza di soluzioni di equazioni paraboliche ed ellittiche , 1968 .

[50]  S. Spagnolo,et al.  Sul limite delle soluzioni di problemi di Cauchy relativi all'equazione del calore , 1967 .