A look at the use of an equivalent homogeneous medium

The technique of homogenization is important in modeling. It allows the scope of the numerical problem to be reduced, thus making the analysis computationally more efficient and allowing the engineer to focus on important larger scale features that influence overall behaviour rather than getting caught up in details that can also lead to numerical difficulties. This paper begins by demonstrating using photoelasticity the importance of taking into account layering details. The inability to capture stress variations due to homogenization is also demonstrated by comparing finite element solutions that take into account details with those which do not. The paper then investigates the consequences of homogenizing a layered system to express its stress–strain response in terms of an equivalent homogeneous anisotropic medium. This is accomplished by analyzing via the finite element method an idealized layered system and comparing the averaged constitutive relation from the numerical solution with that corresponding to an equivalent homogeneous transverse isotropic medium. Thereafter, stress and failure patterns corresponding to a structured medium are examined, as are the consequences of free surfaces and interfaces between layers on the nonhomogeneity of failure.Key words: homogenization, layered soils, photoelasticity, finite element analysis.