Frans van der Meer (Delft University of Technology), Multiscale modeling of composite materials with data-driven surrogates
For computational modeling of the mechanical performance of advanced engineering materials like fiber reinforced composites multiple levels of observations are relevant. For composite laminates, high-fidelity
models have been developed for the mesoscale where individual layers in the laminate are modeled as homogeneous orthotropic material and the microscale where individual fibers embedded in the polymer matrix are modeled explicitly. There is a long-standing vision to couple these scales in concurrent multiscale analysis. However, the coupled multiscale approach comes with excessive computational cost due to the many times the microscopic problem needs to be evaluated. Redundancy in the computational effort associated with the many evaluations of the micromodel potentially offers a way out, namely by creating data-driven surrogates, where the idea is that a smaller number of evaluations could be used to train a surrogate for the micromodel that can give accurate predictions at lower computational cost. However, the path-dependence of the material behavior renders the dimensionality of the training space unbounded, as a consequence of which data-driven surrogates do not generalize well even after being trained on a large amount of data. In this presentation, a short overview of strategies for modeling composite materials at multiple scales is given, after which two approaches are presented that aim at limiting the training burden for data-driven surrogates in the context of multiscale modeling. Firstly, an active learning approach with a Gaussian Process based surrogate, where we exploit the fact that in any given multiscale simulation only a small subspace of the complete microscopic input space is explored. And secondly, a physically recurrent neural network, where we embed classical constitutive models in a neural network to incorporate physics-based memory, allowing for superior generalization.
