ISSN:
1619-6937
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
Notes:
Summary A continuum mechanical model describing rapid shear flow of granular materials as deduced by Jenkins and Savage (1983) [11] from considerations of statistical mechanics is applied to steady plane shear flows down an inclined chute. Depending on the type and form of the physically suggested boundary conditions that are imposed at the base and the free surface, respectively, the emerging boundary value problems permit or prohibit existence of mathematical solutions. For instance, the model does not permit incorporation of an aerodynamic drag and requires special sliding boundary conditions at the base. Cause for the singular behavior is the fact that granular pressure and fluctuation energy vanish simultaneously. Rectification is e.g. possible by including particle density gradients in the constitutive relation of granular stress, but this requires postulation of additional boundary conditions. We present the differential equations and boundary conditions and suggest a procedure of non-dimensionalization which yields the dimensionless parameters governing the problem. Construction of local solutions close to the boundaries by means of Frobenius expansions discloses the singular behavior and yields the basis for the non-existence proof under limiting conditions. Adding to the particle stress a Newtonian viscous contribution is not sufficient to regularize the problem and neither is the form of the stress tensor resulting from Lun et al.'s statistical model that incorporates kinetic terms. The stress tensor must have a term proportional to the dyadic product of the particle concentration gradient with itself. Numerical solution techniques and computational results are given in a companion paper (Hutter, Szidarovszky, Yakowitz, 1986 [9]).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01182542
Permalink