Dynamic patterns of compaction in brittle porous media

When compacting a brittle porous medium—think stepping on fresh snow—patterns develop. Simulations and densification experiments with cereals now provide an understanding of compaction patterns in terms of a lattice model with breakable springs. Brittle porous media exhibit a variety of irreversible patterns during densification, including stationary and moving compaction bands in rocks 1 , 2 , 3 , foams 4 , cereal packs 5 and snow 6 . We have recently found moving compaction bands in cereal packs 5 ; similar bands have been detected in snow 6 . However, the question of generality remains: under what conditions can brittle porous media disclose other densification patterns? Here, using a new heuristic lattice spring model undergoing repeated crushing events, we first predict the possible emergence of new types of dynamic compaction; we then discover and confirm these new patterns experimentally in compressed cereal packs. In total, we distinguish three observed compaction patterns: short-lived erratic compaction bands, multiple oscillatory propagating compaction bands reminiscent of critical phenomena near phase transitions, and diffused irreversible densification. The manifestation of these three different patterns is mapped in a phase diagram using two dimensionless groups that represent fabric collapse and external dissipation.