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• W4319601611 endingPage "851" @default.
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• W4319601611 abstract "Abstract Herein, we present a new data-driven multiscale framework called FE $${}^textrm{ANN}$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msup> <mml:mrow /> <mml:mtext>ANN</mml:mtext> </mml:msup> </mml:math> which is based on two main keystones: the usage of physics-constrained artificial neural networks (ANNs) as macroscopic surrogate models and an autonomous data mining process. Our approach allows the efficient simulation of materials with complex underlying microstructures which reveal an overall anisotropic and nonlinear behavior on the macroscale. Thereby, we restrict ourselves to finite strain hyperelasticity problems for now. By using a set of problem specific invariants as the input of the ANN and the Helmholtz free energy density as the output, several physical principles, e. g., objectivity, material symmetry, compatibility with the balance of angular momentum and thermodynamic consistency are fulfilled a priori. The necessary data for the training of the ANN-based surrogate model, i. e., macroscopic deformations and corresponding stresses, are collected via computational homogenization of representative volume elements (RVEs). Thereby, the core feature of the approach is given by a completely autonomous mining of the required data set within an overall loop. In each iteration of the loop, new data are generated by gathering the macroscopic deformation states from the macroscopic finite element simulation and a subsequently sorting by using the anisotropy class of the considered material. Finally, all unknown deformations are prescribed in the RVE simulation to get the corresponding stresses and thus to extend the data set. The proposed framework consequently allows to reduce the number of time-consuming microscale simulations to a minimum. It is exemplarily applied to several descriptive examples, where a fiber reinforced composite with a highly nonlinear Ogden-type behavior of the individual components is considered. Thereby, a rather high accuracy could be proved by a validation of the approach." @default.
• W4319601611 created "2023-02-09" @default.
• W4319601611 creator A5011405214 @default.
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• W4319601611 creator A5084862505 @default.
• W4319601611 date "2023-02-08" @default.
• W4319601611 modified "2023-09-30" @default.
• W4319601611 title "FE$${}^textrm{ANN}$$: an efficient data-driven multiscale approach based on physics-constrained neural networks and automated data mining" @default.
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• W4319601611 doi "https://doi.org/10.1007/s00466-022-02260-0" @default.
• W4319601611 hasPublicationYear "2023" @default.
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