Multiscale extended computational homogenization for the mechanical design of the advanced materials (MECHMAM): Micro scale strain localization analysis by Minkowski functionals

The main target is extension of the multiscale computational homogenization framework to overcome existing limit in terms of scale separation. Project is dedicated to enrichment of fine-to-coarse and coarse-to-fine transition in multiscale scheme, to obtain fully coupled solution.

Postdoc: O. Gorodetskyi
Supervisor: M.G.D. Geers, M. Hutter
Project Financing: ERC Advanced Grant
Project Period: March 2014 – June 2016

Computational homogenization is an efficient multiscale method for analysing engineering materials, based on solution of coupled problems on the micro- and macroscopic scales. Specifically, the transition between scales is established by averaging the micro scale deformations and stress quantities. Interaction between scales is a key topic in many research areas.

The project aims to establish extended computational homogenization  approach for the cases where conventional scale separation can not be applied. The transition between scales requires certain enrichment to obtain fully coupled solution scheme.

Main attention is concentrated on the fine-to-coarse scale transition. Fine-to-coarse scale transition assumes analysis, decomposition and projection of the micro scale fluctuations on the coarse scale, extending coarse scale description to a generalized micromorphic continuum.

Modelling on a fine scale relies on a microstructural representative volume element (RVE), see Fig.1, on which deformation is imposed. Gradual evolution of the stable uniform material behaviour eventually might lead to the unstable localizing behaviour that requires local analysis of the emerging spatial micro-fluctuation field.

Digital images analysis method (Minkowski functionals) is applied to investigate microfluctuations field. Minkowski functionals analysis aims to analyse morphology of structures captured from digital images, see Fig.2,  and shows wide flexibility to the numerical and experimental study.  Functionals provide fundamental information over the patterns in the images and allows full investigation of their evolution.

Minkowski functionals is an efficient numerical tool for analysing micro scale fluctuations and to detect strain localization.