On solution schemes for time-independent thermomechanical analysis for structures containing polymeric materials

Contradicting ideas about implementing temperature-dependent Young’s modulus in a time-independent quasi-static thermomechanical analysis can be found regularly in the literature. The incremental (quasi-static evolution) and the non-incremental (Hookean) solution schemes represent simplifications of the viscoelastic behavior of polymeric materials according to different theoretical disciplines. These two schemes lead to completely different solutions when Young’s modulus is a function of the temperature. In this paper we review the ideas about implementing temperature-dependent Young’s modulus in a time-independent quasi-static thermomechanical analysis. Differences of the ideologies are highlighted using bimaterial beam solutions. Thermomechanical deformations of a bimaterial structure, which resembles a plastic ball grid array package assembly, at different temperatures are measured using shadow Moiré interferometry. Numerical solutions from different schemes are compared with measurement results.