Force-chain buckling in granular media: a structural mechanics perspective

Parallels are drawn between the response of a discrete strut on a linear elastic foundation and force-chain buckling in a constrained granular medium. Both systems buckle initially into periodic shapes, with wavelengths that depend on relative resistances to lateral displacement, and curvature in the buckled shape. Under increasing end shortening, the classical structural model evolves to a localized form extending over a finite number of contributing links. By analogy, it is conjectured that the granular model of force-chain buckling might follow much the same evolutionary route into a shear band.

[1]  Giles W Hunt,et al.  A general theory of elastic stability , 1973 .

[2]  Giles W Hunt,et al.  FINITE ELEMENT MODELLING OF SPATIALLY CHAOTIC STRUCTURES , 1997 .

[3]  Antoinette Tordesillas,et al.  On the modeling of confined buckling of force chains , 2009 .

[4]  Giles W Hunt,et al.  A nonlinear model for parallel folding with friction , 2003, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[5]  C. J. Budd,et al.  Asymptotics of cellular buckling close to the Maxwell load , 2001, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[6]  Antoinette Tordesillas,et al.  Force chain buckling, unjamming transitions and shear banding in dense granular assemblies , 2007 .

[7]  Thomas F. Fairgrieve,et al.  AUTO 2000 : CONTINUATION AND BIFURCATION SOFTWARE FOR ORDINARY DIFFERENTIAL EQUATIONS (with HomCont) , 1997 .

[8]  Giles W Hunt,et al.  Elastic mimicry of elasto-plastic responses , 1986 .

[9]  E. Knobloch,et al.  Homoclinic snaking: structure and stability. , 2007, Chaos.

[10]  Antoinette Tordesillas,et al.  Buckling force chains in dense granular assemblies: physical and numerical experiments , 2009 .

[11]  M. Ahmer Wadee,et al.  Kink Band Instability in Layered Structures , 2004 .

[12]  G. W. Hunt,et al.  Cellular Buckling in Long Structures , 2000 .

[13]  Giles W Hunt,et al.  Hidden (A)Symmetries of Elastic and Plastic Bifurcation , 1986 .

[14]  G. Hunt.  Buckling in Space and Time , 2006 .

[15]  W. T. Koiter.  THE STABILITY OF ELASTIC EQUILIBRIUM , 1970 .

[16]  Jonathan H. P. Dawes,et al.  Localized Pattern Formation with a Large-Scale Mode: Slanted Snaking , 2008, SIAM J. Appl. Dyn. Syst..

[17]  References , 1971 .