Effective thermal expansion coefficient
          of isotropic multiphase composites and polycrystals

                                   by

                 Leonid Gibiansky, Princeton University


             AEB350,  3:15pm Monday, March 25, 1996

                                Abstract

 The thermal expansion coefficient is the strain that is realized in the
 material when it expands freely due to unit increase in the
 temperature.  We study isotropic multiphase composites made of several
 isotropic phases, and isotropic polycrystals made of crystal grains of
 different orientations. For two-phase composites and polycrystals of
 some groups of symmetry there is a one-to-one correspondence between
 the effective bulk modulus and the effective thermal expansion
 coefficient. For multiphase composites and generic polycrystals one can
 only obtain bounds on the thermal expansion coefficient in terms of the
 bulk modulus of the composite.

 In this talk I will obtain tight bounds on the effective thermal
 expansion coefficients of such isotropic mixtures.  Two and three
 dimensional problems are treated; the results improve upon known bounds
 in both cases. For the polycrystal problem, I will derive the
 conditions that guarantee the one-to-one correspondence between the
 bulk modulus and the effective thermal expansion coefficient of the
 composite; they agree with similar results by Hashin and Schulgasser.

 The derived bounds are also valid for composites with the cubic
 symmetry in three dimensions and composites with the square symmetry in
 2D-problem. Generalization of the results for anisotropic composites of
 anisotropic phases is discussed. All the results can be applied to the
 poroelasticity since the equations of the poroelasticity and the
 thermal expansion are equivalent.

Requests for preprints and reprints to: gibian@cherrypit.princeton.edu
This source can be found at http://www.math.utah.edu/research/