MORPHOLOGICALLY REPRESENTATIVE PATTERN-BASED BOUNDING IN ELASTICITY

A general theory for the homogenization of heterogeneous linear elasti c materials that relies on the concept of ''morphologically representa tive pattern'' is given. It allows the derivation of rigorous bounds f or the effective behaviour of the Voigt-Reuss-type, which apply to any distribution of patterns, or of the Hashin-Shtrikman-type, which are restricted to materials whose pattern distributions are isotropic. Par ticular anisotropic distributions of patterns can also be considered: Hashin-Shtrikman-type bounds for anisotropic media are then generated. The resolution of the homogenization problem leads to a complex compo site inclusion problem with no analytical solution in the general case . Here it is solved by a numerical procedure based on the finite eleme nt method. As an example of possible application, this procedure is us ed to derive new bounds for matrix-inclusion composites with cubic sym metry as well as for transversely isotropic materials.