Fundamentals of the fluctuation-enriched computational homogenization method

Bridging scales in the mechanics of engineering materials is one of the grand challenges in understanding and designing materials bottom-up. This project targets a novel extended multiscale computational homogenization framework, entirely driven by the underlying microstructure through extracted characteristics of the micro-fluctuation field, in order to realize a breakthrough in lifting the existing limits in terms of scale separation.

PhD Candidate: Maqsood M Ameen
Supervisor: Ron Peerlings
Promoter: Marc Geers
Project Financing: ERC
Project Period: August 2014 – July 2018

This work focuses on the theoretical and computational elaboration of the computational homogenization scheme incorporating correlations of the fluctuation field. The lack of scale separation triggers the need for an enriched description at the coarse scale, which can be either generalized micromorphic, or as a special case thereof, purely kinematic. Both cases will be dealt with, where different characteristics of the fluctuations will be considered. This work focuses on quasi-static loading conditions, whereby only spatial fluctuations prevail. A theoretical-computational methodology will be implemented to unravel the relevant part of micro-fluctuation fields causing the breakdown of scale separation. Validation of the method through full scale direct numerical simulations and experiments.  

Investigation of spatially correlated distribution of different fine-scale variables and the coupling of classical continua to micromorphic continua are some of the major challenges in this work.  The model, once implemented and validated, will be of high value especially to composite manufacturing industries.