Two-dimensional plastic flow of a Bingham solid

Source abstract

The rheological equations of state for an isotropic Bingham solid may be written in tensor form: where The notation is explained fully in a previous paper (1). The frame of reference is essentially Eulerian. Primes denote deviatoric components of the stress, strain and rate of strain tensors, p ik , ε ik and e ik (for example, ). The dilatation is denoted by Δ. The rigidity and bulk moduli μ and κ are, if not constants, essentially scalar functions of the stress tensor. The variable viscosity η involves two constants, the yield value ϑ and the reciprocal mobility η 1 .