کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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519579 | 867672 | 2016 | 19 صفحه PDF | دانلود رایگان |
A new manifold-based reduced order model for nonlinear problems in multiscale modeling of heterogeneous hyperelastic materials is presented. The model relies on a global geometric framework for nonlinear dimensionality reduction (Isomap), and the macroscopic loading parameters are linked to the reduced space using a Neural Network. The proposed model provides both homogenization and localization of the multiscale solution in the context of computational homogenization. To construct the manifold, we perform a number of large three-dimensional simulations of a statistically representative unit cell using a parallel finite strain finite element solver. The manifold-based reduced order model is verified using common principles from the machine-learning community. Both homogenization and localization of the multiscale solution are demonstrated on a large three-dimensional example and the local microscopic fields as well as the homogenized macroscopic potential are obtained with acceptable engineering accuracy.
Journal: Journal of Computational Physics - Volume 313, 15 May 2016, Pages 635–653