Abstract
When an amorphous material is strained beyond the point of yielding it enters a state of continual reconfiguration via dissipative, avalanche-like slip events that relieve built-up local stress. However, how the statistics of such events depend on local interactions among the constituent units remains debated. To address this we perform experiments on granular material in which we use particle shape to vary the interactions systematically. Granular material, confined under constant pressure boundary conditions, is uniaxially compressed while stress is measured and internal rearrangements are imaged with x-rays. We introduce volatility, a quantity from economic theory, as a powerful new tool to quantify the magnitude of stress fluctuations, finding systematic, shape-dependent trends. For all 22 investigated shapes the magnitude $s$ of relaxation events is well-fit by a truncated power law distribution $P(s)\sim {s}^{-\tau} exp(-s/s^*)$, as has been proposed within the context of plasticity models. The power law exponent $\tau$ for all shapes tested clusters around $\tau=$ 1.5, within experimental uncertainty covering the range 1.3 - 1.7. The shape independence of $\tau$ and its compatibility with mean field models indicate that the granularity of the system, but not particle shape, modifies the stress redistribution after a slip event away from that of continuum elasticity. Meanwhile, the characteristic maximum event size $s^*$ changes by two orders of magnitude and tracks the shape dependence of volatility. Particle shape in granular materials is therefore a powerful new factor influencing the distance at which an amorphous system operates from scale-free criticality. These experimental results are not captured by current models and suggest a need to reexamine the mechanisms driving mesoscale plastic deformation in amorphous systems.
Highlights
Earthquakes, magnetic avalanches in Barkhausen noise, and sudden slip events during plastic deformation of a granular material are examples of the complex dynamic response of a many-component system that is driven at fixed, slow rate
We focus on mesoscale dynamics, where the length scale of the system is an order of magnitude larger than a characteristic rearrangement event (Fig. 2), but small enough to inhibit shear banding
Similar to what has been reported for other plastically deforming systems [2,5], we find that the shape of the distribution DðsÞ of normalized drop magnitudes s is well fit, for all 22 particle shapes tested, by a truncated power law, DðsÞ ∼ s−τ expð−s=sÃÞ
Summary
Earthquakes, magnetic avalanches in Barkhausen noise, and sudden slip events during plastic deformation of a granular material are examples of the complex dynamic response of a many-component system that is driven at fixed, slow rate. As the applied strain is increased beyond an initial loading phase, the packing yields and eventually enters a regime referred to in soil mechanics as the critical state [32] In this regime the stress has leveled off and fluctuates around a mean value as the packing restructures via nonaffine, dissipative particle rearrangements. Mesoscale granular systems without shear bands offer an excellent test bed for studying the intermittent dynamics of plastic deformation in amorphous materials. In order to quantify the magnitude of sudden stress fluctuations, we introduce a measure borrowed from financial mathematics which quantifies the spread of fractional changes that occur in a time series This measure, volatility, is model independent and is useful in comparing broadly distributed fluctuations in data with different or changing baselines [35]. We discuss the general implications of this behavior in light of recent simulations and mesoscale plasticity models [11] and the opportunities this opens up for designing specific stress responses with granular materials in the regime beyond yielding
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