A Nonintrusive Nonlinear Model Reduction Method for Thermal Cycling-Induced Viscoplastic Deformation Problems Based on Segmented Gaussian Process Regression Machine Learning

Numerical simulation of thermal cycling-induced viscoplastic deformation is important to design a reliable underfilled flip chip package, where the time histories of viscoplastic strains are applied to predict the fatigue life of solder joints. However, the high-fidelity full model simulations of a flip chip package under thermal cycling are time intensive tasks. Nonintrusive model order reduction combined with machine learning is increasingly being used to create efficient surrogate models for problems with high computational costs. In this paper, a segmented Gaussian process regression machine learning method combined with proper orthogonal decomposition is proposed to build the reduced order models of underfilled flip chip packages for thermal cycling-induced viscoplastic displacements and strains, respectively. Simulation results show the derived reduced order models can effectively predict the viscoplastic displacements and strains induced by thermal cycling across the entire solution domain and time history for different material properties of underfills and provide better accuracy than those generated by the non-segmented Gaussian process regression method.