On interactions between imperfections in cellular solids

A number of studies have indicated that imperfections in cellular solids can have a very large influence on their mechanical behavior. Waviness in cell walls can drastically reduce elastic stiffnesses, and various irregularities can reduce the effective strengths by large factors. These imperfections have in many instances been studied in isolation, i.e., only a singe type of imperfection was studied at a time. The goal of the present paper is to shed light on how different kinds of imperfections interact. There is a potential risk that when multiple kinds of imperfections are present, the mechanical properties of the cellular solid are worse than what would be predicted from each one in isolation. The present study is focused on linear elastic properties, although many of the conclusions apply also for other properties. The method employed is based on statistical averages and Taylor expansion arguments. Such techniques have in previous papers been applied to a single imperfection type. The conclusion from the present analysis is that, up to the third order in “small” parameters describing the severity of the imperfections, there is no interaction between a number of different types of imperfections.