Indicators for the Adaptive Choice of Multi-Scale Solvers Based on Configurational Mechanics

For heterogeneous multi-scale methods,different analytical and numerical homogenisation methods can be applied on the micro-level, where the computational domain is a representative volume element (RVE). Several numerical homogenisation algorithms which are based on boundary element approaches, pseudo spectral discretizations, or finite element schemes are available for RVEs. However, each of these methods is only appropriate in subdomains of the macro-scale domain (component), e.g. in low-stress or highly stressed component regions. Therefore, indicators for the adaptive choice of solvers on the micro-scale are helpful. The proposed indicators make use of ideas from configurational mechanics.First of all, configurational forces are introduced as indicators. Then the multi-scale approach for configurational forces is explained and illustrated with an example. Afterwards the application of the configurational forces as an indicator for a refined homogenisation method is demonstrated. The last section is devoted to the scalability of heterogeneous multi-scale computations on parallel computers. A parallel finite element code is used for the macro-scale, and a PYTHON interface for the coupling with the different micro-scale solvers is described.