A thermodynamic framework for the superplastic response of materials

Over the years, a number of constitutive equations have been proposed to model the ther-momechanical behaviour of superplastic materials. Most of those relations were motivated by phenemenological observations and restricted to uniaxial forms at (high homologous) superplastic temperatures. Not only do they lack the rigor of mechanics (e.g. finite deformation, frame invariance, three dimensional form) but also do not potrary the post-formed room temperature response. The latter is an important criterion in determining if a superplastically formed component can be used in a critical industrial application. In this work, we attempt to address these concerns by developing superplastic constitutive relationships within the frame work of nonlinear mechanics and thermodynamics by invoking the concept of natural configurations. This is an imposing but important task. This work (the first in a series of papers) outlines the basic principles of such a formulation and enumerates the restrictions arising from the structural and mechanical observations of superplastic materials in different temperature regimes.