CONSTITUTIVE EQUATIONS FOR THE COMPUTING PERSON I thank Dr. N. Phan-Thien and Dr. M. B. Bush for help with this research, which was supported by the Australian Research Grants Scheme. I also thank the Mathematics Research Center for hospitality during 1984

Publisher Summary This chapter discusses some of the precautions required while choosing a constitutive equation when setting out to do computing. Depending on the kinematic problem in hand, one of the several mathematical representations of the material can be chosen. The chapter discusses the behavior of (1) rate-type equations; (2) Green–Rivlin or integral type expansions, and (3) differential constitutive equations. The rate-type equations include the Criminale–Ericksen-Filbey equation, which is an exact representation of isotropic fluid behavior in viscometric flows. The chapter describes the stability of the rheological problem. Sometimes, there might be genuine flow instability, which is observable experimentally. Another cause of problems is lack of convergence because of inadequate numerical schemes. However, assuming that these problems have been avoided, there still remains the possibility that the description of the material, constitutive equation, chosen is the cause of lack of convergence.