Abstract
We present a lumped model to study the rotational modes in a type of two-dimensional periodic solid composites comprised of a square array of rubber-coated steel cylinders embedded in an epoxy matrix. The model captures the physical essence of rotational modes in such systems for various combinations of material parameters, and, therefore it is able to describe the transition behaviour when the system is gradually adjusted from an elastic metamaterial to an elastic phononic crystal. From the model, we can define a transition zone which separates the typical elastic metamaterials and the phononic crystals.