Guo, T.

Veroy, K.

Scipedia

8th ECCOMAS Thematic Conference on the Mechanical Response of Composites: COMPOSITES 2021M. Fagerström & G. Catalanotti (Editors)ACCELERATING TWO-SCALE SIMULATIONS WITH ANON-INTRUSIVE REDUCED ORDER MODELTheron Guo1∗, Karen Veroy11 Centre for Analysis, Scientific Computing and ApplicationsDepartment for Mathematics and Computer ScienceEindhoven University of Technology∗ E-mail: t.guo@tue.nlIn order to understand the structure-property relations of complex materials, two-scale materialsimulations utilizing computational homogenization can be used. In computational homoge-nization the microstructure is explicitly defined on a so-called representative volume element,hence replacing the macroscopic constitutive model and yielding a coupled formulation whichcan be solved with a multilevel finite element scheme. Due to high computational expenses,such simulations can be infeasible in multi-query contexts such as optimization, control or de-sign. To make such analyses possible, in this work, a surrogate model for the microscopicsimulation based on reduced basis methods [1] is proposed. After a few high-fidelity simula-tions have been computed and collected, the surrogate is constructed in two steps. In the firststep, a proper orthogonal decomposition is applied on the stress field to extract a global low-dimensional basis that can sufficiently approximate the stress. Then, a regression based on deepneural networks [2, 3] is employed to find the basis coefficients for any parameter. Given any ar-bitrary new parameter, the microscopic field is rapidly obtained, from which the effective stressand stiffness can be analytically derived. Furthermore, the derivatives of the stress with respectto material parameters are readily available and can thus be used for optimization or design. Toillustrate the accuracy of the surrogate model, a two-scale problem involving a fiber-reinforcedcomposite microstructure is presented. The macroscopic solution obtained with the surrogatemodel is compared to the full two-scale simulation. The results showcase the high accuracy ofthe proposed method on both macro- and microscale despite using a relatively small trainingdataset and highlight the high efficiency of the method.Acknowledgement: This result is part of a project that has received funding from the EuropeanResearch Council (ERC) under the European Union’s Horizon 2020 research and innovationprogramme (Grant agreement No. 818473).References[1] Quarteroni, A., Manzoni, A. and Negri, F., 2015. Reduced basis methods for partial dif-ferential equations: an introduction (Vol. 92). Springer.[2] Hesthaven, J.S. and Ubbiali, S., 2018. Non-intrusive reduced order modeling of nonlinearproblems using neural networks. Journal of Computational Physics, 363, pp.55-78.[3] Mohan, A.T. and Gaitonde, D.V., 2018. A deep learning based approach to reduced or-der modeling for turbulent flow control using LSTM neural networks. arXiv preprintarXiv:1804.09269.

Accelerating two-scale Simulations with a Non-intrusive Reduced Order Model

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Accelerating two-scale Simulations with a Non-intrusive Reduced Order Model

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