Bounding the Multi-Scale Domain in Numerical Modelling and Meta-Heuristics Optimization: Application to Poroelastic Media with Damageable Cracks.

It is very common for natural or synthetic materials to be characterized by a periodic or quasi-periodic micro-structure. This micro-structure, under the different loading conditions may play an important role on the apparent, macroscopic behaviour of the material. Although, fine, detailed information can be implemented at the micro-structure level, it still remains a challenging task to obtain experimental metrics at this scale. In this work, a constitutive law obtained by the asymptotic homogenization of a cracked, damageable, poroelastic medium is first evaluated for multi-scale use. For a given range of micro-scale parameters, due to the complex mechanical behaviour at micro-scale, such multi-scale approaches are needed to describe the (macro) material's behaviour. To overcome possible limitations regarding input data, meta-heuristics are used to calibrate the micro-scale parameters targeted on a synthetic failure envelope. Results show the validity of the approach to model micro-fractured materials such as coal or crystalline rocks.