COUPLED ESTIMATES FOR THE BULK AND SHEAR MODULI OF A 2-DIMENSIONAL ISOTROPIC ELASTIC COMPOSITE

WE IMPROVE the classical Hashin-Shtrikman and Walpole estimates of the effective properties for an isotropic mixture assembled from two isot ropic elastic materials. The planar elasticity problem is considered. Unlike the prior estimates which bound the bulk and shear moduli indep endently, our estimates are coupled and more restrictive. The set of t he bulk modulus-shear modulus pairs turns out to be bounded in the pla ne of the values of these moduli by two straight lines (the Hashin-Sht rikman or Walpole bulk modulus estimates) and also by two fractional l inear curves. To obtain the new estimates we use the translation metho d, which provides a general approach to both Hashin-Shtrikman (well-or dered materials) and Walpole (badly-ordered materials) cases; the meth od also provides the estimates for anisotropic mixtures.