Waveform memory in random grain packs*

Using numerical simulations it is shown that a jammed, random pack of soft frictional grains can store an arbitrary waveform that is applied as a small time-dependent shear while the system is slowly compressed. When the system is decompressed at a later time, an approximation of the input waveform is recalled in time-reversed order as shear stresses on the system boundaries. By varying the friction coefficient and friction model, it is shown that this memory effect depends essentially on friction between the grains. A simple but non-quantitative explanation is proposed based on the storage of bulk sample shear as frictional stresses in the individual contacts that form while the sample is being compressed. The memory effect is present for the simplest (Cundall-Strack) model of friction as well as for a more elaborate model that captures the history dependence of Mindlin-Deresiewicz theory, but it is absent for an intermediate model that has frequently been used in granular simulations. The dependence of memory storage on sample size, degree of compression, and stored waveform complexity is explored. This type of memory could potentially be observable in other types of random media that form internal contacts when compressed such as crumpled sheets and fiber nests or bundles.