Toward stochastic multi-scale methods in continuum solid mechanics

The scientific community has realised that non-determinism is a major issue that affects
structural and material performance and reliability. Because experimental characterisation
alone cannot reliably sample the tails of distributions, virtual stochastic testing has thus become
a research field of growing interest. Since the uncertainties at the structural level also
result from the variability of the micro-structure, there is a need to develop computationally
efficient stochastic multi-scale methods. The purpose of this work is to provide a summary
of the different methods that have been developed in the context of micro-structure characterisation and reconstruction, of stochastic homogenisation and of uncertainties up-scaling.