Energy transport and dissipation in granular systems

The study of energy transport in granular systems can involve a number of different angles to view the problem; for example, one can propagate sinusoidal waves within the granular assembly, which makes the particles vibrate; besides the large wavelength low-amplitude elastic limit, this can be at very large frequencies and medium-large amplitudes, thereby posing the particles in perturbations of different modes, like resulting in cyclic shear, which can be translational and/or rotational as well as oblique collisions between the particles to occur. If these particles are naturally occurring grains, they will have a far from classical "elastic" response and their morphologies will be evolving during these perturbations. If a viscous fluid is added, then the dynamics of these perturbations and the way the energy is transferred among the particles may be substantially different. One may wish to see this problem even at a smaller scale, examining only two perturbating particles in contact, or allowing them to impact each other in the presence of a fluid. If you load the granular system in a cyclic mode, but this time at a very low frequency, some mechanisms will be altered, and the way the energy will be dissipated may also be expected to be altered, thereby the interpretations made from such analysis. Of course, a granular assembly is often part of a larger system that we are interested in to study by stability analysis, as e.g. internal erosion, or the dynamics of a submarine landslide involving an extraordinarily large span of particle sizes and morphologies. Taking as example research works in soil dynamics, the rate of stiffness decrease in a granular system, caused by the nonlinearity of that system, is proportional to the rate of energy dissipation increase as macroscopically measured in medium-frequency torsional shear dynamic excitation. However, if the excitation amplitude is reduced enough to lead to measurements of elastic stiffness, some small dissipation of energy might still be observed, which generally contradicts principles of classic continuum mechanics. These, and many others are interesting and exciting, though challenging areas of research in granular matter, in which scientists from a wide span of expertise are working to provide answers, and perhaps raise more questions about what is happening in a granular system. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023