Existing formulations for material modeling are not integrated fully with thermal behavior. Apart from the ignorable thermoelastic effects, they do not provide insight into the variation of basic parameters such as the elastic modulus with temperature.

Traditional constitutive models attempt to derive the governing equation for a material element as a single phase. The successful use of continuum damage and its extensions for describing degradation suggests exploration of similar schemes for constitutive modeling.

This work applies the principle of superposition of phases to constitutive modeling, to obtain generalized stress-strain‑temperature relationships which describe the elastic, plastic and creep behavior of solder and other materials under various temperature and strain rates, based on material parameters that are independent of temperature and strain rate. Material behavior is expressed as a superposition of the behavior of simplified phases, which are attained in asymptotic limits, such as at zero absolute temperature and zero strain, and at extremely high temperature and sufficiently large strain so as to make the interatomic forces negligible. Phases are separated in a manner so as to ensure energy balance.

Details of derivations are in Dube (2004). Only the final equations, which are to be treated as empirical equations, with their validity determined by the results of their prediction, are provided here, along with examples for Aluminum, Lead and Tin for the thermoelastic case. Results for solder were obtained for the thermoelastic case, as well as for plastic yield and creep deformation. References for the slideshow are in the references page.