New Transient and Pseudo-Transient Algorithms for Viscoelastic Materials

Abstract : The principal investigator, D. S. Malkus, his post-doctoral associate, and Ph.D. students worked on three projects related to AFOSR research: (1) Planar viscoelastic flows of fluids with integral constitutive equations. The purpose of the project was to develop new algorithms for flows of non-Newtonian fluids and use them to study polymer-processing flows. (2) Simulation and analysis of differential infrared thermographic stress analysis-- SPATE. A consistent thermodynamic theory of viscoplasticity was developed and methods for the experimental determination of model parameters were proposed. The consequence of viscoplastic behavior on differential thermography was studied, by simulating the SPATE stress analysis system. (3) Optimal mass in the finite element method. The purpose of the project was to explore the feasibility and usefulness of quadrature-based optimal mass matrix lumping techniques for higher-order finite element schemes, where they often produce indefinite but diagonal mass matrices.