Manu Dube, Ph.D.
The University of Arizona, 2004

Advisor: Prof. T. Kundu

Modeling simplifications for complex material behavior may lead to unanticipated errors under generalized loading conditions, which are difficult to detect in finite element analyses. This work analyzes existing models under simple loading conditions where the nature of the results is known a priori, and proposes new models to overcome the limitations detected. Elastic and elastoplastic formulations for loading dependent material parameters are generalized, and limitations of the rate dependent elastoplastic simulation and the Perzyna viscoplastic formulation are discussed. A yield function that provides continuous yielding irrespective of the direction of loading and does not generate spurious plastic strain increments under temperature change is developed. A thermomechanical model based on the concept of superposition of asymptotic phases is also proposed, with generalized stress-strain-temperature relationships that intrinsically predict the variation of the coefficient of thermal expansion and elastic constants with temperature. These are validated for aluminum, lead, tin and solder. A plastic yield criterion shown to be in general agreement with hardening based on dislocation density and a preliminary empirical creep equation for lead tin eutectic solder are developed as part of the thermomechanical model. Finally an approximate dissipated work based formulation for the Disturbed State Concept of Desai (2001) is developed and limitations of DSC assumptions are discussed. Validations are conducted for the eutectic lead tin data of Wang et al. (2001), with prior parameters being shown to require recomputation.