Effect of out-of-plane material behavior on in-plane modeling

In the analysis of the thermo-mechanical behavior of multi-layered structures in electronic packages, three-dimensional (3D) models often serve as the most accurate representations. However, 3D analyses are usually computationally intensive and time-consuming. Therefore, two-dimensional (2D) models with appropriate assumptions and boundary conditions are often used in the thermomechanical analysis of electronic packaging assemblies. A significant cause for concern for such 2D simplification is the role of the out-of-plane coefficient of thermal expansion. This paper analyzes the role of the out-of-plane CTE in thermo-mechanical modeling through the use of plane-strain, plane-stress, 3D, and generalized deformation numerical models along with closed-form analytical formulations. A special plane-strain case with the out-of-plane CTE set to be zero has also been studied.