Luigi La Ragione, Giuseppina Recchia, Felix Darve, Francois Nicot, Antoine Wautier
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Abstract
We consider a dense aggregate of elastic, frictional particles isotropically compressed and next uniaxial strained at constant pressure. We show how failure can be predicted if fluctuations in the kinematics of contacting particles are introduced. We focus on the second order work and the possibility that at some stressed states it becomes negative under proper perturbations. Our analysis involves both a theoretical model and numerical simulations based upon the distinct element method (DEM). The theoretical model deals with contacting particles with incremental relative displacements that deviate from the average deformation in order to ensure their equilibrium. Because of this, the macroscopic stiffness tensor of the aggregate, that relates increments in stress with increments in strain, does not have the major symmetry. Consequently, in the hardening regime, we predict stressed states in which the second order work vanishes. The model seems transparent, and it makes clear and illustrative the role played by the fluctuations introduced in the kinematics of contacting particles in relation to the vanishing of second order work in an aggregate of compressed particles. The comparison with numerical simulations data supports the model.
Graphical Abstract
Statistical representation of the aggregate: conditional average.
期刊介绍：
Although many phenomena observed in granular materials are still not yet fully understood, important contributions have been made to further our understanding using modern tools from statistical mechanics, micro-mechanics, and computational science.
These modern tools apply to disordered systems, phase transitions, instabilities or intermittent behavior and the performance of discrete particle simulations.
>> Until now, however, many of these results were only to be found scattered throughout the literature. Physicists are often unaware of the theories and results published by engineers or other fields - and vice versa.
The journal Granular Matter thus serves as an interdisciplinary platform of communication among researchers of various disciplines who are involved in the basic research on granular media. It helps to establish a common language and gather articles under one single roof that up to now have been spread over many journals in a variety of fields. Notwithstanding, highly applied or technical work is beyond the scope of this journal.
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