A comparison of homogenization and standard mechanics analyses for periodic porous composites

Abstraet. Composite material elastic behavior has been studied using many approaches, all of which are based on the concept of a Representative Volume Element (RVE). Most methods accurately estimate effective elastic properties when the ratio of the RVE size to the global structural dimensions, denoted here as ~/, goes to zero. However, many composites are loeally periodic with finite q. The purpose of this paper was to compare homogenization and standard mechanics RVE based analyses for periodie porous composites with finite ~/. Both methods were implemented using a displacement based finite element formulation. For one-dimensional analyses of composite bars the two methods were equivalent. However, for twoand three-dimensional analyses the methods were quite different due to the fact that the local RVE stress and strain state was not determined uniquely by the applied boundary conditions. For two-dimensional analyses of porous periodic eomposites the effective material properties predicted by standard meehanics approaehes using multiple cell RVEs converged to the homogenization predietions using one cell. In addition, homogenization estimates of loeal strain energy density were within 30% of direct analyses while standard mechanics approaehes generally differed from direct analyses by more than 70%. These results suggest that homogenizataon theory is preferable over standard mechanics of materials approaches for periodic composites even when the material is only locally periodic and q is finite.