A Data-driven Multiscale Analysis by Combination of Cluster-based Non-uniform Transformation Field Analysis and Artificial Neural Network

Data-driven computational mechanics have been used in the field of multiscale analysis where the constitutive modeling of composites is obtained by learning the material database obtained experimentally or numerically, using artificial neural network (ANN). In this paper, we present a data-driven multiscale analysis by combining the cluster-based non-uniform transformation field analysis (CNTFA), a reduced order model for the numerical homogenization of composites with periodically arranged microstructure, with ANN. Here, the CNTFA which was developed by the authors is efficient reduced order model for multiscale analysis of different nonlinear composites. Feed-forward neural network, a neural network is designed and trained for calculating the material stiffness and reproducing the microscale field quantities. The stiffness of homogenized material is approximately calculated using the gradient of ANN and strain concentration tensor. The proposed method can be effectively used in reproduction of field information (e.g. strain and stress) at the microscale as well as the analysis of structures at the macroscale. This property is distinguished with other cluster based methods such as SCA, VCA, FCA, in which the field information is reproduced at cluster level, not microscale level. An example calculation of three-point bending beam shows that the proposed method is very effective for the multiscale analysis of nonlinear composite structures.