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Elastomeric mechanical metamaterials exhibit unconventional mechanicalbehaviour owing to their complex microstructures. A clear transition in theeffective properties emerges under compressive loading, which is triggered bylocal instabilities and pattern transformations of the underlying cellularmicrostructure. Such transformations trigger a non-local mechanical responseresulting in strong size effects. For predictive modelling of engineeringapplications, the effective homogenized material properties are generally ofinterest. For mechanical metamaterials, these can be obtained in an expensivemanner by ensemble averaging of the direct numerical simulations for a seriesof translated microstructures, applicable especially in the regime of smallseparation of scales. To circumvent this expensive step, computationalhomogenization methods are of benefit, employing volume averaging instead.Classical first-order computational homogenization, which relies on thestandard separation of scales principle, is unable to capture any size andboundary effects. Second-order computational homogenization has the ability tocapture strain gradient effects at the macro-scale, thus accounting for thepresence of non-localities. Another alternative is micromorphic computationalhomogenization scheme, which is tailored to pattern-transforming metamaterialsby incorporating prior kinematic knowledge. In this contribution, a systematicstudy is performed, assessing the predictive ability of computationalhomogenization schemes in the realm of elastomeric metamaterials. Threerepresentative examples with distinct mechanical loading are employed for thispurpose: uniform compression and bending of an infinite specimen, andcompression of a finite specimen. Qualitative and quantitative analyses areperformed for each of the load cases where the ensemble average solution is setas a reference.

Enriched Computational Homogenization Schemes Applied to Pattern-Transforming Elastomeric Mechanical Metamaterials