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

Abstract

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.Comment: 32 pages, 19 figures, 1 table, abstract shortened to fulfil 1920 character limi