A constitutive model for porous media with recurring stress drops: From snow to foams and cereals

Abstract

Porous media such as dry snow, cellular foams, or cereals, can experience abrupt and recurrent drops in stress when subjected to mechanical loading. While there appears to be little agreement on the initiating mechanism of stress drops, it is well-accepted that they correlate with the destruction of the meso-scale structure of the material. However, this observation has yet to supply a general predictive way to accommodate these stress drops at the constitutive level for porous media. Here, we develop a constitutive model to explain such behaviour in dry conditions. The model builds upon the concept of meso-related temperature, which characterises the fluctuating velocities of the meso-scale structure and is general to all heterogeneous porous media. We assume that a rise in meso-related temperature induces a loss of strength at the macro-scale, which leads to a stress drop. Furthermore, the meso-related temperature sinks into micro-related (thermal) temperature and thus allows for stress recovery after a drop. Our model exhibits different behaviours and stress drop regimes from these basic physical concepts, providing insight into previous experimental observations in porous media. While this is not an exhaustive model for any of the materials listed, it can provide a potential starting point for all of them.