A rational formulation of the equations of plastic flow for a Bingham solid

Abstract

In this paper we are concerned with a material which can support a finite stress elastically without flow and which flows with constant mobility(1) (or plastic fluidity) when the stresses are sufficiently great. Following Bingham(1) and Houwink(2), such a material is called a Bingham solid and the type of flow (purely) plastic. The transition from elastic to plastic behaviour takes place at the yield point.

Issues in the flow of yield-stress liquids

“…Properly invariant three-dimensional constitutive equations for the Bingham fluid were introduced by Oldroyd (1947) and Prager (1961). Oldroyd's formulation assumes that the material is a linearly elastic solid at stresses below the yield criterion, where the yield surface is defined by a von Mises criterion.…”

The blocking of an inhomogeneous Bingham fluid. Applications to landslides

“…The Bingham model, also denominated "Bingham solid" (see for instance [20]) was considered in order to describe the deformation of many solid bodies. In metal-forming processes, it was introduced for wire drawing in [3] and intensively studied in [4,13].…”

“Everything flows?”: elastic effects on startup flows of yield-stress fluids

“…Barnes (1999) has written a comprehensive review of the history of the study of yielding, in which he places the common yield-stress fluids currently being studied in the context of phenomena like creep in metals and plastics. Modern interest in yieldstress fluids largely dates from work by Oldroyd (1947) and Prager (Hohenemser and Prager 1932;Prager 1961) that put the description of such material s into an invariant continuum formulation that can be applied to flows in complex geometries. Both Oldroyd and Prager assumed that there is a transition between a solid and a fluid at a critical value of a stress invariant, typically taken to be a yield surface defined by the von Mises criterion (Prager 1961).…”