Effective constitutive properties of linear elastic cellular solids with randomly oriented cells

A new methodology to derive the linear effective constitutive law for a group of composites with random microstructure of a special kind is described as an extension of the methodology proposed in Warren and Kraynik (1988) and of the methodology used in polycrystal theory. The results are expressed in the form of specific bounds on effective elastic constants. Practical importance is in the specific bounds when the methodology is applied to cellular solids. Several examples are shown and compared with other published results. The new contribution of this paper lies in the presentation of the methodology, derivation of new specific bounds in two dimensions, and comments related to already published works on cellular solids.