Leibniz MMS Days 2025 - Key Note Lecture
van der Meer, Frans (TU Delft)
The development and use of new materials is key for reducing the resources required for engineering structures. Fiber reinforced composite materials form an example, combining low weight with high mechanical performance and good durability. However, predicting their long-term performance is challenging, which leads to high safety factors or expensive testing requirements. Moreover, the lack of reliable and efficient predictive models stands in the way of optimization of the material design. One of the challenging aspects is that the spatial scale on which the material response can be accurately described is lower than the scale of interest for structural analysis. For non-linear problems, accuracy cannot be maintained after direct upscaling of microscale model results to the macroscale, and multiscale analysis with two-way coupling is needed. However, multiscale analysis with high-fidelity models at two (or more) scales comes with excessive computational cost. Data-driven surrogates for the lower scale models are an appealing option to accelerate the multiscale framework, but can only be reliable if the surrogate is trained on sufficient data, where very large data requirements potentially defeat the purpose of building the efficient surrogate. In this presentation, a recently proposed surrogate modeling strategy, the physically recurrent neural network (PRNN), is presented, which offers high accuracy with limited training data by embedding the physics-based constitutive models from the microscale in a neural network. The surrogate model is applied to a challenging multiscale case for the analysis of the time-dependent response of thermoplastic composites. It is furthermore demonstrated that the architecture of the PRNN allows to even go beyond multiscale analysis toward multiscale uncertainty quantification.