Quasi-Analytic Sensitivity Analysis of a Unified Viscoplastic Constitutive Model for a Solder Alloy

Unified constitutive models for the consistent description of inelastic thermomechanical response of engineering alloys to widely varying control conditions are strongly nonlinear; there are numerous constants to be determined; and successful use depends critically on expert professional judgment. These circumstances are not unlike those associated with the design of complex systems dependent on successful interaction of multidisciplinary teams. Introduced in this paper is a paradigm for design of constitutive models motivated by modern system design methodologies. Specifically, a quasi-analytic sensitivity analysis is applied to a special form of a viscoplasticity-based overstress model (VBO) for the uniaxial, isothermal, high-homologous temperature mechanical response of a solder alloy. Parameter sensitivity is demonstrated via linear algebraic equations. The technique is a critical first step to application of sophisticated techniques of multidisciplinary design optimization (MDO) to constitutive modeling.