A nonlinear manifold-based reduced order model for multiscale analysis of heterogeneous hyperelastic materials

JOURNAL OF COMPUTATIONAL PHYSICS

卷:313

Article

Bhattacharjee, Satyaki¹  Matous, Karel¹ 

[1] Univ Notre Dame, Dept Aerosp & Mech Engn, Notre Dame, IN 46556 USA

关键词: Computational homogenization;    Nonlinear manifold;    Reduced order model;    Machine learning;    Parallel computing;   

DOI  :  10.1016/j.jcp.2016.01.040

来源: Elsevier

【 摘 要 】

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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free