Instability in the evolution equations describing incompressible granular flow
Constitutive equations for incompressible granular materials are derived and analyzed. Raw materials are often stored and moved in granular form, so there is considerable interest in mathematical theories that can be applied to engineering design. The author gives a detailed derivation of the equations governing incompressible rigid-perfectly plastic Coulomb powders, using a von Mises type yield condition. The equations formally resemble the Navier-Stokes equations, but are homogeneous of degree zero in the strain rate tensor. The equations then are linearized, exponentially unstable solutions are identified, and the steady state equations are analyzed (which need not be of elliptic type). These results are then applied to a well-known similarity solution (Jenike's radial solution), which is shown to lead to ill-posed problems in most practical applications. The paper concludes with a discussion of other possible constitutive laws, including compressible materials, and of oscillatory motions which are observed in industrial silos.
incompressible rigid-perfectly plastic Coulomb powders
scientific article; zbMATH DE number 4056161