Micro-macro Modeling of Particle Crushing Based on Branch Lengths
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A micro-macro model of particle crushing is proposed. Microstructure changes are tracked with the density and size distribution of branch lengths. At the scale of a representative elementary volume (REV), the free energy density of a set of branches of same length is written as the product of the total deformation energy stored in the REV by an energy split function, assumed to follow a power law. The distribution of deformation energy stored by the branches of a granular assembly subjected to isotropic compression is calculated with PFC3D discrete element method (DEM) program. The main findings of this paper are that this distribution varies indeed with branch lengths and that the power law provides a good fit for an exponent of three. A macroscopic crushing parameter is defined to follow the progress of particle comminution (and therefore, dissipation). Constraints on the expression of the dissipation potential associated to particle crushing are explained to ensure the convexity of the elastic domain. The proposed framework is expected to improve current thermodynamic models of particle crushing based on grain size distributions (GSDs), especially to predict "shielding effects." This framework can be tested by DEM modeling of particles crushing, and better energy estimates could be used to optimize processes to make powders in the pharmaceutical and food industry.