Dimensional reduction technique for the prediction of global and local responses of unidirectional composite with matrix nonlinearity and varying fiber packing geometry

Abstract

The problem associated with the computational homogenization of composite materials often results in expensive computational cost that prevents engineers from comprehensive study for better understanding of composite behaviors, especially when nonlinear effects are considered. While variation in local fiber arrangements has pronounced effect on damage initiation and failure mechanisms in composite, an attempt to reduce the computational cost for the parametric study of such a problem seems to be absent. This paper demonstrates the capability of a model order reduction (MOR) framework to accelerate the parametric study of the unidirectional composite with a plastic constitutive material model for matrix with the varying fiber distribution in the microstructure as the parameter of interest. The MOR framework used in this work is based on the construction of the reduced order basis (ROB) by proper orthogonal decomposition and then the reduced order model (ROM) by Galerkin projection. The concept of local ROB is incorporated which helps decreasing further the dimension of the ROM and, thus, the computational cost. The results from the RVE-based high-fidelity finite element analysis and from the ROM are compared to assess the efficiency and accuracy of the approach. Notable computational gain is achieved with the potential to improve further in the future work. The error in the global response is less than 10% while the local stress fields in the critical regions can be captured well which paves way for the extension to consider the process of damage initiation and evolution as the source of nonlinearity in the future.