Submodeling Analysis for Path-Dependent Thermomechanical Problems

In a finite element analysis, when localized behavior of a large model is of particular concern, generally one would refine the mesh until it captures the local solution adequately. Submodeling is an alternative way for solving this kind of problem. It provides a relatively accurate solution at a modest computational cost. For a valid submodeling analysis, the boundaries of the submodel should be sufficiently far away from local features so that St. Venant’s principle holds. Moreover, special treatments are required for solving problems that involve path-dependent characteristics. This paper presents a general procedure to perform submodeling analyses for path-dependent thermomechanical problems without a priori assumptions on the structural response. The procedure was benchmarked using a bimaterial strip and demonstrated through analyses on a bump chip carrier package assembly. The procedure is conducive to the numerical assessment of fatigue lives of electronic packages.