Using Superelement Model in Active Thermal Cycle with Temperature Dependent Properties

Superelement (SE) is a modeling technique where the assembled stiffness matrix of a fully meshed model is reduced to a smaller subset of master degrees of freedom (DOFs) while condensing out internal DOFs with methods like Guyan reduction. The reduced stiffness matrix and its remaining master DOFs act as one SE in subsequent analysis to represent the stiffness behavior of the original meshed model. SE can be used to obfuscate critical intellectual property (IP) in the chip package design including internal geometry and part material properties, creating an obfuscated version of the chip that can be shared and used in board-level reliability simulations. However, traditional SE implementation based on Guyan reduction leads to a constant SE reduced stiffness matrix, therefore, it is not able to account for temperature-dependent material properties which have significant effects during thermal cycling. Previous research explored superimposing multiple SEs, each evaluated at a different (albeit uniform) temperature to capture temperature-dependent material properties in passive thermal cycling. This presentation expands on this concept and explores an extension to active thermal cycling where the temperature distribution within the chip package is not uniform. Using a generic example model, we demonstrated convergence to the full solid element behavior. A sensitivity study is performed to demonstrate robustness of the proposed method with respect to material property variations.