In recent years, considerable progress has been made in bridging the mechanics of materials to the structural engineering level supported by advances in multi-scale modelling. Different classes of computational scale bridging methods have been developed to this purpose, spanning different disciplines, e.g. engineering, computational mechanics, mathematics, physics, chemistry etc. Although these methods have usually been equipped for a specific research problem, from a methodological point of view, similarities and distinctive features can be identified. Just a few examples include (i) methods that either rely on the separation of scales principle, or directly embed the fine scale model in the course scale one, leading to either nested or concurrent solution procedure; (ii) two-way coupling (fine-coarse and vice versa) or one-way (fine scale informed coarse scale model); (iii) the use of fine scale models for either extracting new emerging phenomena at the coarse scale, or quantification of the a-priori known coarse scale behaviour.

This colloquium intends to serve as a forum for bringing together scientists from different disciplines working on scale bridging problems (both spatial as well as temporal) in materials and structures. The colloquium aims to identify common and distinct features of different techniques as well as their limitations and upcoming challenges, in order to stimulate and initiate an interdisciplinary cross-fertilisation.

The topics addressed in this colloquium will include:

• homogenization based methods, e.g. mathematical homogenization, computational homogenization etc.
• embedded domain methods, domain decomposition methods, global-local technique
• heterogeneous multi-scale method (HMM), equation-free method
• (non-equilibrium) thermodynamics based coarse graining methods
• methods for bridging distinct models, e.g. atomistics-to-continuum
• methods for phenomena with (partially) non-separating scales, e.g. localization, damage and fracture or transient phenomena
• methods for coupled multi-field phenomena (e.g. thermo-chemo-electro-mechanical etc.)
• methods for interfaces and contact conditions
• model reduction techniques and reduction of computational costs associated with multiscale algorithms and complex microstructures, e.g. arising from experimental imaging techniques