Abstract
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.
Similar content being viewed by others
References
R. Hill (1950) The Mathematical Theory of Plasticity Oxford University Press Oxford 356
W. Prager P.G. Hodge (1951) Theory of Perfectly Plastic Solids Wiley New York 264
L. Prandtl (1923) ArticleTitleAnwendungsbeispiele zu einem Henckyshen Satz über das plastische Gleichgewicht Z. angew Math. Mech. 3 401–406
Hartmann W. (1925). Über die Integration der Differentialgleichungen des ebenen Gleichgewiichtszustandes für den Allgemein-Plastichen Körper. Thesis, Gottingen
E.A. Marshall (1967) ArticleTitleThe compression of a slab of ideal soil between rough plates Acta Mech. 3 82–92
A.J.M. Spencer (1964) ArticleTitleA theory of the kinematics of ideal soils under plane strain conditions J. Mech. Phys. Solids 12 337–351
A.J.M. Spencer (1982) Deformation of ideal granular materials H.G. Hopkins M.J. Sewell (Eds) Mechanics of Solids; the Rodney Hill Anniversary Volume Pergamon Press Oxford 607–652
A.J.M. Spencer (2003) ArticleTitleDouble-shearing theory applied to instability and localization in granular materials J. Engng. Math. 45 55–74
A.J.M. Spencer (1986) ArticleTitleInstability of shear flows of granular materials Acta Mech. 64 77–87
J.C. Savage D.A. Lockner J.D. Byerlee (1996) ArticleTitleFailure in laboratory fault models in triaxial tests J. Geophys. Res. 101 22215–22224
J.R. Rice (1992) Fault stress state, pore pressure distributions, and the weakness of the San Andreas fault B. Evans T.-F. Wong (Eds) Fault Mechanics and Transport Properties in Rocks Academic Press San Diego 475–503
P.A. Gremaud (2004) ArticleTitleNumerical issues in plasticity models for granular flows J. Volcanology & Geothermal Res. 137 1–9
S. Alexandrov (2003) ArticleTitleCompression of double-shearing and coaxial models for pressure-dependent plastic flow at frictional boundaries J. Appl. Mech. 70 212–219
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
A.J.M. Spencer M.R. Kingston (1973) ArticleTitlePlane mechanics and kinematics of compressible ideal granular materials Rheol. Acta 12 194–199
M.M. Mehrabadi S.C. Cowin (1978) ArticleTitleInitial planar deformation of dilatant granular materials J.Mech.Phys. Solids 26 269–284
M.M. Mehrabadi S.C. Cowin (1980) ArticleTitlePre-failure and post-failure soil plasticity models J. Engng. Mech. Div. Proc ASCE 106 991–1003
R. Hill E.H. Lee S.J. Tupper (1951) ArticleTitleA method of numerical analysis of plastic flow in plane strain and its application to the compression of a ductile material between rough plates J. Appl. Mech. 8 46–52
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Spencer, A.J.M. Compression and shear of a layer of granular material. J Eng Math 52, 251–264 (2005). https://doi.org/10.1007/s10665-004-5662-9
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10665-004-5662-9