Multiphase composites with extremal bulk modulus
The paper is devoted to the long-standing problem on bounds on effective properties of elastic composites made of isotropic phases. An analytical and a numerical study are performed to examine the ranges of effective bulk and shear moduli. For two-phase composites it is shown that the bounds are attainable, that is, there exist composites with extreme bulk and shear moduli. For multiphase composites the bounds may be or may not be attainable, depending on phase moduli and volume fractions. A numerical topology optimization procedure that solves the inverse homogenization problem is adopted and used to look for two-dimensional three-phase composites with a maximal effective bulk modulus. New types of microstructures with bulk moduli close to the bound are found numerically for the situations where the attainability conditions are not met.
scientific article; zbMATH DE number 1487041
scientific article