  This paper focuses on size effects in periodic mechanical metamaterials
driven by reversible pattern transformations due to local elastic buckling
instabilities in their microstructure. Two distinct loading cases are studied:
compression and bending, in which the material exhibits pattern transformation
in the whole structure or only partially. The ratio between the height of the
specimen and the size of a unit cell is defined as the scale ratio. A family of
shifted microstructures, corresponding to all possible arrangements of the
microstructure relative to the external boundary, is considered in order to
determine the ensemble averaged solution computed for each scale ratio. In the
compression case, the top and the bottom edges of the specimens are fully
constrained, which introduces boundary layers with restricted pattern
transformation. In the bending case, the top and bottom edges are free
boundaries resulting in compliant boundary layers, whereas additional size
effects emerge from imposed strain gradient. For comparison, the classical
homogenization solution is computed and shown to match well with the ensemble
averaged numerical solution only for very large scale ratios. For smaller scale
ratios, where a size effect dominates, the classical homogenization no longer
applies.
