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On micro-to-macro transitions for multi-scale analysis of non-linear heterogeneous materials: unified variational basis and finite element implementation

This article introduces for the first time a unified variational basis underpinning multi-scale analysis of generic non-linear heterogeneous materials. The theoretical and algorithmic framework presented in this article will have a major impact on the finite element based multi-scale analysis with a wide range of applications in science and engineering. The research is a result of collaboration with Professor Feijoo, based in National Laboratory for Computational Mechanics, Brazil. The research was partially funded by the EPSRC Grant (EP/D500281), and the main results were presented by Prof Peric in Plenary Lecture at the 10th International Conference on Computational Plasticity, Barcelona.