Compression and shear of a layer of granular material. (English) Zbl 1079.74018

Spencer, A. J. M.

J. Eng. Math. 52, No. 1-3, 251-264 (2005).

Summary: A classical problem in metal plasticity is the compression of a block of material between rigid platens. The corresponding problem for a layer of granular material that conforms to the Coulomb-Mohr yield condition and the double-shearing theory for the velocity field has also been solved. A layer of granular material between rough rigid plates that is subjected to both compression and shearing forces is considered. Analytical solutions are obtained for the stress and velocity fields in the layer. The known solutions for steady simple shear and pure compression are recovered as special cases. Yield loads are determined for combined compression and shear in the case of Coulomb friction boundary conditions. Numerical results which describe the stress and velocity fields in terms of the normal and shear forces on the layer at yield are presented for the case in which the surfaces of the platens are perfectly rough. Post-yield behaviour is briefly considered.

MSC:

74E20	Granularity
74G05	Explicit solutions of equilibrium problems in solid mechanics

Keywords:

Coulomb-Mohr yield condition; double-shearing theory; Coulomb friction

References:

[4]	Hartmann W. (1925). Über die Integration der Differentialgleichungen des ebenen Gleichgewiichtszustandes für den Allgemein-Plastichen Körper. Thesis, Gottingen
[14]	Huaning Zhu, M.M. Mehrabadi and M. Massoudi. (2002). A comparative study of the response of double shearing and hypoplastic models. In: Proceedings of IMECE: 2002 ASME International Mechanical Engineering Congress and Exposition, New Orleans Amer. Soc. Mech. Engrs., Materials Div. Publ. MD Vol. 97. pp. 343–351