Reduced order homogenization of thermoelastic materials with strong temperature-dependence and comparison to a machine-learned model

Abstract In this work, an approach for strongly temperature-dependent thermoelastic homogenization is presented. It is based on computational homogenization paired with reduced order models (ROM) that allow for full temperature dependence of material parameters in all phases. In order to keep the model accurate and computationally efficient at the same time, we suggest the use of different ROMs at few discrete temperatures. Then, for intermediate temperatures, we derive an energy optimal basis emerging from the available ones. The reduced homogenization problem can then be solved in real-time. Other than in classical homogenization where only the effective behavior, i.e. the effective stiffness and the effective thermal expansion, of the microscopic reference volume element (RVE) are of interest, our ROM delivers also accurate full-field reconstructions of all mechanical fields on the RVE scale. We show that the proposed method referred to as optimal field interpolation is on par with linear interpolation in terms of its numerical cost but with an accuracy that matches direct numerical simulation (DNS) in many cases, i.e. very accurate real-time predictions are anticipated with minimal DNS inputs that range from two to six temperatures at which simulations are pursued. Further, we pick up a black box machine-learned model as an alternative route and show its limitations in view of the limited training data.