A model order reduction approach to construct efficient and reliable virtual charts in computational homogenisation

Introduction Computational homogenisation is a widely spread technique to calculate the overall properties of a composite material from the knowledge of the constitutive laws of its microscopic constituents [1, 2]. Indeed, it relies on fewer assumptions than analytical or semi-analytical homogenisation approaches and can be used to coarse-grain a large range of micro-mechanical models. However, this accuracy comes at large computational costs, which prevents computational homogenisation from being used routinely in optimisation, even in the context of linear elastic materials. Indeed, a unit cell problem has to be solved for each microscopic distribution of interest in order to obtain the corresponding homogenised material constants. In the context of nonlinear, time-dependant problem, the computational effort becomes even greater as computational homogenisation requires solving for the time-evolution of the microstructure at every point of the macroscopic domain.