The Simulation of Three-Dimensional Metalforming Processes Using State Variable Constitutive Models for Large Strain, Viscoplastic Flow at Elevated Temperature (Finite Elements, Internal Variable)

Date of Award


Document Type


Degree Name

Doctor of Philosophy (Ph.D.)

Institution Granting Degree

Cornell University

Cedarville University School or Department

Engineering and Computer Science


Mechanical engineering


Two state variable constitutive models for the plastic flow of metals are implemented in a three-dimensional, finite-element code, entitled ISAIAH, for the modeling of metalforming processes. ISAIAH utilizes a steady state approach with an Eulerian reference frame. A viscoplastic flow law for a linear viscous fluid is assumed and thermomechanical coupling with viscous dissipation is included. The two models implemented in ISAIAH are those proposed by Anand and Hart. Anand's model is implemented in its complete form while Hart's model is implemented in a simplified form in which the anelastic strain is neglected; this form is applicable at elevated temperatures. ISAIAH is used to model three-dimensional, shaped rolling in the high temperature regime. A baseline simulation is performed as well as many parameter variations which examine the overall effect of changes in roll speed, inlet temperature, percent reduction, and mesh refinement. The two state variable models are used to predict the deformations and stresses for the steady state. Special attention is given to the integration of the evolutionary equation of the state variable. A comparison of the material behavior predicted by the two constitutive models for the simulations is presented as is a comparison of the computational behavior of the two models.