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MECHMAM Report Summary

Project ID: 339392
Funded under: FP7-IDEAS-ERC
Country: Netherlands

Mid-Term Report Summary - MECHMAM (Multiscale Extended Computational Homogenization for the Mechanical design of Advanced Materials)

The project MECHMAM addresses a fundamental challenge in bridging scales in the mechanics of engineering materials, requiring a breakthrough in lifting the existing limits in terms of scale separation. The projects targets a novel extended multiscale homogenization framework, in order to realize its objectives. The prime application field of the project are advanced mechanical metamaterials, exploiting complex interactions between the scales involved.

The major breakthrough realized in the first term of this project, concerns the multiscale model for acoustic metamaterials (AM). These materials have specially fabricated microstructures capable of advanced manipulation of sound waves such as band-pass filtering, redirection, channelling, multiplexing etc. that is otherwise impossible to achieve using ordinary materials. Within MECHMAM a novel and versatile numerical multi-scale technique has been developed for the simulation and analysis of complex elasto-dynamics of acoustic metamaterials. A homogenization technique for modelling materials with local resonances is proposed, resulting in an accurate description of the effective macroscopic continuum in a low frequency regime. To this end, the concept of so-called computational homogenization, well-established for the macroscale modelling of heterogeneous composite materials in a quasi-static regime, was extended to the transient case. Using model reduction tools, a compact closed form description of the micro-dynamics has been obtained that accurately captures the local resonance phenomena. The resulting equations constitute an enriched (micromorphic) continuum in which additional kinematic degrees of freedom emerge to account for local resonance effects which would otherwise be absent in a classical continuum. Such an approach offers a new framework for developing numerical solution schemes that are vastly more computationally efficient in comparison to traditional approaches without any reduction in accuracy. Moreover, this result enabled the development of a multiscale semi-analytical analysis technique for locally resonant acoustic metamaterials, allowing for fast transmission and dispersion analysis for arbitrary and complex micro-structure designs. It is expected that this achievement can lead to a significant speed-up of the design and rapid prototyping of this specific type of metamaterials. This major achievement is accompanied by material design-oriented research, revealing the role of visco-elasticity in an acoustic metamaterial.

Other achievements in the project are mainly scientific in nature. This mainly concerns that identification and extraction of micro-fluctuation fields in heterogeneous materials (e.g. higher-order fluctuations in the strains, or strain localization patterns). Three methods have been developed for that purpose: (1) a method relying on mathematical homogenization techniques; (2) a method using imaging analysis and statistical measures, applicable to images of either experimental or numerical nature; (3) a novel global digital imaging correlation technique, which identifies extracts pre-defined fluctuation patterns of experimental images (as required to remove imaging artefacts). These scientific building stones will be further exploited in the project to overcome other scale separation limits in the multi-scale analysis of heterogeneous materials involving small scale instabilities and discontinuities. Since the MECHMAM project requires extensive computational resources, progress is being made in improved model reduction schemes as well, whereby the adopted research direction is oriented towards the development of a wavelet-based reduction at the level of the microstructural calculations.

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