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 di used irreversible densification. The manifestation of these three di erent patterns is mapped in a phase diagram using two dimensionless groups that represent fabric collapse and external dissipation.Compaction of brittle porous media is of central importance in industry and science, and has many ramifications, from destruction waves during meteoritic impacts 7 to the formation of density heterogeneities in pharmaceutical pills 8 and permeability barriers in rocks 9,10 . Previous work on brittle porous media has generally revealed two forms of compaction patterns: stationary and oscillatory propagating compaction bands. Specifically, stationary compaction bands with localized intense volumetric strain rate have been frequently observed in a wide range of brittle porous materials, including rocks 1-3 , foams 4 and honeycomb materials 11 . The formation of such bands has been rationalized mathematically using continuum models of viscoplasticity 12,13 or breakage mechanics 14,15 , with the latter connecting the process directly to the physics of grain breakage and pore collapse.The formation of oscillatory propagating compaction bands in porous media was discovered more recently by Valdes et al.5 , via uniaxially confined compression experiments on puffed rice packs (Fig. 1a). Similar to stationary compaction bands, the material within these bands experienced high volumetric strain rates accommodated by severe grain breakage and pore collapse. By comparing experiments on material placed in containers with different boundary roughness, this work motivated a connection between compaction dynamics to how energy is dissipated outside.More recently, similar experiments on dry foamy snow 6 also revealed oscillatory propagating compaction bands, although with only one or two oscillations per test (this will be discussed later, in Fig. 2g-i). This form of compaction was captured using a phenomenological continuum model for snow, with an assumed elastoplastic yield function, power-law density dependence, shearinduced bond failure, strength recovery due to sintering, and nonlocality of damage 6 . The need for these assumptions indicates that the underlying mechanisms that control the emergence of oscillatory compaction bands are not clear yet.In this paper we present experiments that unfold novel compaction patterns in brittle porous media. We show that all the observed patterns can be explained using a simple lattice spring model. We then map the manifested patterns in terms of a phase diagram that covers system and material parameters, applicable for brittle porous...

Compaction of brittle porous material leads to a wide variety of densification patterns. Static compaction bands occurs naturally in rocks or bones, and have important consequences in industry for the manufacturing of powder tablets or metallic foams for example. Recently, oscillatory compaction bands have been observed in brittle porous media like snow or cereals. We will discuss the great variety of densification patterns arising during the compaction of puffed rice, including erratic compaction at low velocity, one or several travelling compaction bands at medium velocity and homogeneous compaction at larger velocity. The conditions of existence of each pattern are studied thanks to a numerical spring lattice model undergoing breakage and is mapped to the phase diagram of the patterns based on dimensionless characteristic quantities. This also allows to rationalise the evolution of the compaction behaviour during a single test. Finally, the localisation of compaction bands is linked to the strain rate sensitivity of the material.