Non-Intrusive Two-Way Coupling for Multiscale Analysis of Electronic Packages

A common approach to modeling failure phenomena in multi-scale electronic packages is by building a global model of the entire package from which boundary conditions for a local, detailed model are extracted. As the failure phenomena at local scale evolves, the boundary conditions are typically not altered, that is, the application of boundary conditions is "one-way," which often yields inaccurate behavioral evolution at the local scale. Instead, in this paper, a two-way coupling non-intrusive computational strategy for iterative solution to the nonlinear behavior in the sub-domains is proposed. To estimate the residual force on the interface connecting the sub-domains, with possibly non-matching discretizations, variational principles with an intermediate framework are proposed to assure satisfaction of the virtual work principle in the subdomains and to assure displacement/traction compatibility at the interface. To map nodal force from one subdomain to the other, both global Lagrange multiplier (GLM) and local Lagrange multiplier (LLM) methods are discussed. Symmetric Rank 1 update as well as the BFGS update are considered for accelerating the solution convergence. The developed method is suitable for the modular construction of sub-models with non-matching discretizations, thereby allowing one to create a reusable library of models for future use. This method even allows coupling between sub-domains analyzed using different (commercial or custom) finite element codes. The iterative global-local coupling strategy is validated on several examples starting with a simple L-shaped domain with local non-linearity and a rectangular plate with a propagating crack. The developed strategy is then demonstrated on crack propagation in solder alloys within packages where its increased accuracy compared to conventional one-way coupling becomes evidently clear. Another example illustrating the coupling of domains independently analyzed using commercial finite element codes ANSYS and ABAQUS is demonstrated. Finally, the method is demonstrated to analyze semiconductor chip assemblies where plastic ratcheting of the interconnect line causes passivation coating fracture.