Energy distribution during the quasi-static confined comminution of granular materials

A method is proposed to calculate the distribution of energy during the quasi-static confined comminution of particulate assemblies. The work input, calculated by integrating the load-displacement curve, is written as the sum of the elastic deformation energy, the breakage energy and the redistribution energy. Experimental results obtained on samples subjected to compression stresses ranging between 0.4 and 92 MPa are used to calibrate the model. The elastic energy stored in the samples is obtained by simulating the compression test on the final particle size distributions (PSDs) with the discrete element method and by extracting the contact forces. A PSD evolution law is proposed to account for particle breakage. The PSD is related to the total particle surface in the sample, which allows calculating the breakage energy. The redistribution energy, which comprises the kinetic energy of particles being rearranged and the friction energy dissipated at contacts, is obtained by subtracting the elastic energy and breakage energy from the work input. Results show that: (1) at least 60% of the work input is dissipated by particle redistribution; (2) the fraction of elastic deformation energy increases, and the fraction of redistribution energy decreases as the compression stress increases; (3) the breakage energy accounts for less than 5% of the total input energy, and this value is independent of the compressive stress; (4) the energy dissipated by redistribution is between 14 and 30 times larger than the breakage energy.