Data-driven surrogate models for an efficient numerical homogenization of open-porous biopolymer aerogels
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The highly open-porous nanostructure of biopolymer aerogels presents a significant challenge for simulating their mechanical properties. Traditional computational methods that explicitly account for their nanostructured morphology and subsequent numerical simulations are computationally expensive. To overcome this limitation, multiscale numerical homogenization approaches are commonly employed to account for the coupling effects of a heterogeneous nanostructure and macroscopic deformations. Based on the well-established FE$^2$ method we apply a homogenization approach which couples the aerogel nanostructure with a finite element solver at the macroscopic scale. For biopolymer aerogels, modelling the representative volume element (RVE) as a beam frame model has proven to be suitable. However, computing the microscopic problem for typical aerogel nanostructures requires solving many large systems of equations. Replacing the microscopic beam frame model with a computationally cheaper surrogate model yields significant potential for reducing the computational effort of the homogenization method. Machine learning techniques are used to train a model which predicts the resulting average stress in an aerogel RVE for a given macroscopic deformation.
