On the use of internal variable constitutive equations in transient forming processes (Q1081357)

Constitutive relations which utilize internal variables to characterize the changing state of a material during a deformation process have been proposed by several investigators in recent years. The internal variable models offer the advantage of extending the range of conditions over which a single material description is applicable at the computational cost of integrating the evolution equations for the internal variables. A method is presented for including a constitutive equation utilizing a single scalar internal variable in a model for transient thermomechanical phenomena. Galerkin's method is used to obtain the finite-element formulation for the time integration of the evolution equation. As an illustration of the technique Hart's model is implemented in a simplified form where the anelastic strain has been neglected leaving only the scalar internal variable. A method for determining material parameters is outlined in the context of a particular material (304 Stainless Steel). The material parameters are determined entirely from data independent of the application.