SCALE EFFECTS IN MEDIA WITH PERIODIC AND NEARLY PERIODIC MICROSTRUCTURES, PART I - MACROSCOPIC PROPERTIES

Traditional averaging and homogenization techniques, developed to pred ict the macroscopic properties of heterogeneous media, typically ignor e microstructure related scale effects-that is, the influence of the s ize of the representative volume, relative to the size of the unit cel l. This issue is presently investigated by exploring the behavior of a nonlinearly elastic, planar lattice model, which is subjected to gene ral macroscopic deformations. For these materials, scale effects may b e due to nonuniformities in the macroscopic strain field throughout th e specimen, or alternatively, to the presence of microstructural imper fections that may be either geometric or constitutive in nature. For t he case of macroscopic strain nonuniformities, if is shown that the mi crostructure related scale effects can be accounted for by the presenc e of higher-order gradient terms in the macroscopic strain energy dens ity of the model. For the case of microstructural imperfections, the d ifference between the respective macroscopic properties of the perfect and imperfect models are shown to depend on the relative size of the specimen, and on the imperfection amplitude and wavelength, while bein g nearly insensitive to the imposed macroscopic strain. For all of the cases considered, several analytical approximations are proposed to p redict the influence of scale on the macroscopic properties, and the a ccuracy of each method is examined.