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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
R. Hill, The Mathematical Theory of Plasticity. Oxford: Oxford University Press (1950) 356 pp.
W. Prager and P.G. Hodge, Theory of Perfectly Plastic Solids. New York: Wiley (1951) 264 pp.
L. Prandtl, Anwendungsbeispiele zu einem Henckyshen Satz über das plastische Gleichgewicht. Z. angew Math. Mech. 3 (1923) 401–406.
W. Hartmann, Über die Integration der Differentialgleichungen des ebenen Gleichgewiichtszustandes für den Allgemein-Plastichen Körper. Thesis: Gottingen (1925).
E.A. Marshall, The compression of a slab of ideal soil between rough plates. Acta Mech. 3 (1967) 82–92.
A.J.M. Spencer, A theory of the kinematics of ideal soils under plane strain conditions. J. Mech. Phys. Solids 12 (1964) 337–351.
A.J.M. Spencer, Deformation of ideal granular materials. In: H.G. Hopkins and M.J. Sewell (eds.), Mechanics of Solids; the Rodney Hill Anniversary Volume. Oxford: Pergamon Press (1982) pp. 607–652.
A.J.M. Spencer, Double-shearing theory applied to instability and localization in granular materials. J. Engng. Math. 45 (2003) 55–74.
A.J.M. Spencer, Instability of shear flows of granular materials. Acta Mech. 64 (1986) 77–87.
J.C. Savage, D.A. Lockner and J.D. Byerlee, Failure in laboratory fault models in triaxial tests. J. Geophys. Res. 101 (1996) 22215–22224.
J.R. Rice, Fault stress state, pore pressure distributions, and the weakness of the San Andreas fault. In: B. Evans and T.-F. Wong (eds.), Fault Mechanics and Transport Properties in Rocks. San Diego: Academic Press 1992) pp. 475–503.
P.A. Gremaud, Numerical issues in plasticity models for granular flows. J. Volcanology & Geothermal Res. 137 (2004) 1–9
S. Alexandrov, Compression of double-shearing and coaxial models for pressure-dependent plastic flow at frictional boundaries. J. Appl. Mech. 70 (2003) 212–219.
Huaning Zhu, M.M. Mehrabadi and M. Massoudi, 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 (2002) pp. 343–351.
A.J.M. Spencer and M.R. Kingston, Plane mechanics and kinematics of compressible ideal granular materials. Rheol. Acta 12 (1973) 194–199.
M.M. Mehrabadi and S.C. Cowin, Initial planar deformation of dilatant granular materials. J.Mech.Phys. Solids 26 (1978) 269–284.
M.M. Mehrabadi and S.C. Cowin, Pre-failure and post-failure soil plasticity models. J. Engng. Mech. Div. Proc ASCE 106 (1980) 991–1003.
R. Hill, E.H. Lee and S.J. Tupper, A 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 (1951) 46–52.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer
About this chapter
Cite this chapter
Spencer, A. (2005). Compression and shear of a layer of granular material. In: Hill, J.M., Selvadurai, A. (eds) Mathematics and Mechanics of Granular Materials. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4183-7_14
Download citation
DOI: https://doi.org/10.1007/1-4020-4183-7_14
Received:
Accepted:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3781-8
Online ISBN: 978-1-4020-4183-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)