Hysteresis, aging, return-point memory, energy dissipation, congruence, and avalanches in uniaxially stressed bi-dispersed frictional disks

We present measurements of the axial compression of bi-dispersed frictional disks in a planar array that display aging, hysteresis, and sub-loop congruence such as occur in magnetic systems or in the behavior of sedimentary rock. The disks are manufactured from thermoplastic material with height 1 cm and diameters 1.0 and 1.5 cm. The friction between disks is determined by different sets asperities on the radial outer surface. Opposing sides of a rectangular cage of width W=1 m and length L=0.5 m are displaced in small steps Δx ~ 0.25 μm resulting in strain increments ε = Δx/L ~ 10^-6 and in compressive forces measured by force transducers. Acoustic excitation could be provided with varying spectral composition and amplitude. The position of each disk was determined by a set of high-resolution cameras which were also used to determine local forces through bi-refringence measurements when photo-elastic disks were used. Starting from a random initial distribution of disks, compression/decompression cycles exhibit aging. After some cycles one obtains a repeatable hysteresis loop for the stress-strain curves that exhibits return-point memory and congruence of small loop segments within the larger overall cycle. The energy dissipation is determined by the area encompassed by the compression/decompression curves and is found to scale linearly with the available energy ~ ΔεΔσ where σ is the uniaxial stress. The hysteresis arises from small rearrangements - "avalaches" - of local disks that are held in place by both elastic and frictional forces (there is no hysteresis for purely elastic interactions). Evidence for local small scale disk motions is seen in small global stress-strain events and through visual observations of disk motions. Many of our observations are consistent with a Preisach model of hysteretic behavior.