New original research article accepted for publication
Shadi Sharba, Julius Herb and Felix Fritzen are happy to announce a new article entitled "Reduced order homogenization of thermoelastic materials with strong temperature-dependence and comparison to a machine-learned model" to appear in Archives Of Applied Mechanics. The article is now available online here (OpenAccess).
Authors
- Shadi Sharba
- Julius Herb
- Felix Fritzen
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 (ROMs) 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 resulting reduced homogenization problem can be solved in real-time.
Unlike 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 within the microstructure.
We show that the proposed method referred to as optimal field interpolation is computationally as efficient as simplistic linear interpolation. However, our method yields an accuracy that matches direct numerical simulation (DNS) in many cases, i.e., very accurate real-time predictions are achieved. Additionally, we propose a greedy sampling procedure yielding a minimal number of direct numerical simulations as inputs (two to six discrete temperatures are used over a range of around 1000 K). Further, we pick up a black box machine-learned model as an alternative route and show its limitations in view of the limited amount of training data. Using our new method to generate an abundance of data we demonstrate that a highly accurate tabular interpolator can be gained easily.
Please cite as
Sharba, S., Herb, J. & Fritzen, F. Reduced order homogenization of thermoelastic materials with strong temperature- dependence and comparison to a machine-learned model. Archives Of Applied Mechanics (published online April 21, 2023). DOI: 10.1007/s00419-023-02411-6