Constitutive Model of a Transversely Isotropic Bingham Fluid

Abstract

A constitutive theory is presented for a transversely isotropic, viscoplastic (Bingham) fluid. The theory accounts for threshold (yield) and viscous flow characteristics through inclusion of a potential function serving the dual role of a threshold function and a viscous flow potential. The arguments and form of the potential function derive from the theory of tensorial invariants. The model reduces to a transversely isotropic model of perfect plasticity in the limit of vanishing viscosity. In the limit of isotropy, it reduces to the Hohenemser-Prager generalization of Bingham’s model. A characterization procedure is prescribed based on correlation with experiments conducted under simple states of stress. Application is made to polymer melts filled with talc particles.