  Elastomeric mechanical metamaterials exhibit unconventional mechanical
behaviour owing to their complex microstructures. A clear transition in the
effective properties emerges under compressive loading, which is triggered by
local instabilities and pattern transformations of the underlying cellular
microstructure. Such transformations trigger a non-local mechanical response
resulting in strong size effects. For predictive modelling of engineering
applications, the effective homogenized material properties are generally of
interest. For mechanical metamaterials, these can be obtained in an expensive
manner by ensemble averaging of the direct numerical simulations for a series
of translated microstructures, applicable especially in the regime of small
separation of scales. To circumvent this expensive step, computational
homogenization methods are of benefit, employing volume averaging instead.
Classical first-order computational homogenization, which relies on the
standard separation of scales principle, is unable to capture any size and
boundary effects. Second-order computational homogenization has the ability to
capture strain gradient effects at the macro-scale, thus accounting for the
presence of non-localities. Another alternative is micromorphic computational
homogenization scheme, which is tailored to pattern-transforming metamaterials
by incorporating prior kinematic knowledge. In this contribution, a systematic
study is performed, assessing the predictive ability of computational
homogenization schemes in the realm of elastomeric metamaterials. Three
representative examples with distinct mechanical loading are employed for this
purpose: uniform compression and bending of an infinite specimen, and
compression of a finite specimen. Qualitative and quantitative analyses are
performed for each of the load cases where the ensemble average solution is set
as a reference.
