Abstract
The question of how soft granular matter, or dense amorphous systems, re-arrange their microstructure under isotropic compression and de-compression, at different strain rates, will be answered by particle simulations of frictionless model systems in a periodic three-dimensional cuboid. Starting compression below jamming, the systems experience the well known jamming transition, with characteristic evolutions of the state variables elastic energy, elastic stress, coordination number, and elastic moduli. For large strain rates, kinetic energy comes into play and the evolution is more dynamic. In contrast, at extremely slow deformation, the system relaxes to hyper-elastic states, with well-defined elastic moduli, in static equilibrium between irreversible (plastic) re-arrangement events, discrete in time. Small, finite strains explore those reversible (elastic) states, before larger strains push the system into new states, by irreversible, sudden re-arrangements of the micro-structure.
Highlights
The question of how soft granular matter, or dense amorphous systems, re-arrange their microstructure under isotropic compression and de-compression, at different strain rates, will be answered by particle simulations of frictionless model systems in a periodic three-dimensional cuboid
1 Introduction while at the same time the periodic cell size changes, In non-Newtonian systems, complex fluids [1], colloidal suspensions, [2], and especially granular matter in its flowing states [3], the transport coefficients depend on various state-variables such as the density and the granular temperature [4]
The bulk modulus, B, in Fig. 4, only shows up for the two slowest simulations, due to the small, arbitrary E0, and not much differences can be seen in the elastic modulus, only the peaks that indicate plastic, irreversible rearrangement events are different
Summary
P dp/kn, in Fig. 1, shows not much differences between the different rates, even for the largest rate it is only a tiny bit larger. The energy ratio, Ek/Ep, in Fig. 2, is strongly rate dependent, with approximately two orders of magnitude difference between simulations that feature different rates with factors of 10 between each other. The coordination numbers, C∗, in Fig. 3, are very similar, only the fastest simulation slightly undershoots the others, but on this scale not much differences can be seen. The bulk (tangent) modulus, B, in Fig. 4, only shows up for the two slowest simulations, due to the small, arbitrary E0, and not much differences can be seen in the elastic modulus, only the peaks that indicate plastic, irreversible rearrangement events are different. Note that the peaks on the unloading branch are much less frequent due to the higher stability of previously precompressed packings, consistent with previous results, see Ref. [12] and references therein
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