A comparative study of enriched computational homogenization schemes applied to two-dimensional pattern-transforming elastomeric mechanical metamaterials

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Samenvatting

Elastomeric mechanical metamaterials exhibit unconventional behaviour, emerging from their microstructures often deforming in a highly nonlinear and unstable manner. Such microstructural pattern transformations lead to non-local behaviour and induce abrupt changes in the effective properties, beneficial for engineering applications. To avoid expensive simulations fully resolving the underlying microstructure, homogenization methods are employed. In this contribution, a systematic comparative study is performed, assessing the predictive capability of several computational homogenization schemes in the realm of two-dimensional elastomeric metamaterials with a square stacking of circular holes. In particular, classical first-order and two enriched schemes of second-order and micromorphic cmoputational homogenziation type are compared with ensemble-averaged full direct numerical simulations on three examples: uniform compression and bending of an infinite specimen, and compression of a finite specimen. It is shown that although the second-order scheme provides good qualitative predictions, it fails in accurately capturing bifurcation strains and slightly over-predicts the homogenized response. The micromorphic method provides the most accurate prediction for tested examples, although soft boundary layers induce large errors at small scale ratios. The first-order scheme yields good predictions for high separations of scales, but suffers from convergence issues, especially when localization occurs.

Originele taal-2Engels
TijdschriftComputational Mechanics
VolumeXX
Nummer van het tijdschriftX
Vroegere onlinedatum11 jan. 2024
DOI's
StatusE-publicatie vóór gedrukte publicatie - 11 jan. 2024

Financiering

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement No [339392] and from the Czech Science Foundation (GAČR) grant agreement No [19-26143X] (O. Rokoš 03/2019–12/2019). The authors would furthermore like to thank Maqsood M. Ameen for numerous fruitful discussions in the early stages of the project, related to micromorphic computational homogenization.

FinanciersFinanciernummer
Seventh Framework Programme
European Research Council339392
Grantová Agentura České Republiky03/2019–12/2019, 19-26143X

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