A hyper-reduction computational method for accelerated modeling of thermal cycling-induced plastic deformations

For materials under cyclic thermal loadings, temperature and strain rate-dependent creep deformation can occur due to the thermal expansion mismatch near material interfaces, leading to deterioration of fatigue life. Simulation of the nonlinear mechanical deformation processes of materials subjected to thermal cycling with high-fidelity numerical models often consume high computational costs due to material nonlinearities and long thermal loading period. To accelerate such thermal cycling simulation, an efficient reduced-order modeling framework is proposed. We adopt the reproducing kernel particle method (RKPM) to generate offline high-fidelity model snapshots, which are utilized to create low-dimensional surrogate models based on the proper orthogonal decomposition under Galerkin projection. Based on the stabilized conforming nodal integration technique, gradient smoothing at single integration point per integration cell is employed in conjunction with a least-squares stabilization for high computational efficiency. To further speed up the simulation, a hyper-reduction method is introduced to avoid the full domain integration during the elastoplastic online simulation. Numerical examples on modeling of thermal cycling-induced plastic deformation and thermal fatigue life prediction of a flip chip assembly are analyzed to demonstrate the effectiveness of the present hyper-reduced-order model in significant reduction of computational time while preserving desired accuracy.