Analogy Between the Groundstate of an Antiferromagnet and the Mode of Quasi-Static Deformation of a Packing of Spheres


We report on local and global processes during the mechanical deformation of packings of spheres. We demonstrate that solid friction imposes a counter-rotation interaction to two adjacent grains during the deformation in order to minimize losses. This is equivalent to introduce an anti-ferromagnetic spin-like interaction in the structure; the search for the deformation process is quite similar to that one of finding the groundstate of an anti-ferromagnetic disordered structure with special boundary conditions. We demonstrate experimentally that boundaries may produce leading frustration processes; in this case, they govern most of the deformation mode and cancel mostly the influence of bulk mechanical properties (at least in the case when global “antiferromagnetic” order of the bulk is allowed by the absence of frustration). Frustration due to triangular local structure is described and existence of “anti-ferromagnetic-like” domains is proved; these domains are induced by the adequation between the boundary conditions and the deformation process and the domain wall is a stress-localization band as named in classical soil mechanics.

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We thank Prof. J. BIAREZ for kind advices and encouragements and Dr D. SORNETTE for very stimulating and encouraging discussions. This work has been supported by GRECO-géomatériaux. P.E. wants to thank E.S.A. for partial financial support.

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Evesque, P. Analogy Between the Groundstate of an Antiferromagnet and the Mode of Quasi-Static Deformation of a Packing of Spheres. MRS Online Proceedings Library 291, 97–102 (1992).

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