Linking initial microstructure and local response during quasistatic granular compaction.

We performed experiments combining three-dimensional x-ray diffraction and x-ray computed tomography to explore the relationship between microstructure and local force and strain during quasistatic granular compaction. We found that initial void space around a grain and contact coordination number before compaction can be used to predict regions vulnerable to above-average local force and strain at later stages of compaction. We also found correlations between void space around a grain and coordination number, and between grain stress and maximum interparticle force, at all stages of compaction. Finally, we observed grains that fracture to have an above-average initial local void space and a below-average initial coordination number. Our findings provide (1) a detailed description of microstructure evolution during quasistatic granular compaction, (2) an approach for identifying regions vulnerable to large values of strain and interparticle force, and (3) methods for identifying regions of a material with large interparticle forces and coordination numbers from measurements of grain stress and local porosity.

Propagation of rarefaction pulses in discrete materials with strain-softening behavior.

We report on the dynamic behavior of strongly nonlinear discrete materials with anomalous strain-softening behavior. Rarefaction solitary waves found in numerical calculations agree well with the exact solution to the continuum wave equation. Compression pulses generated by impact quickly disintegrate into a leading rarefaction solitary wave followed by an oscillatory wave train containing localized excitations. Such behavior is favorable for metamaterials design of shock absorption layers as well as tunable information transmission lines for scrambling of acoustic information.

Shock wave structure in a strongly nonlinear lattice with viscous dissipation.

The shock wave structure in a one-dimensional lattice (e.g., granular chain of elastic particles) with a power law dependence of force on displacement between particles (F proportional to delta(n)) with viscous dissipation is considered and compared to the corresponding long wave approximation. A dissipative term depending on the relative velocity between neighboring particles is included to investigate its influence on the shape of a steady shock. The critical viscosity coefficient p(c), defining the transition from an oscillatory to a monotonic shock profile in strongly nonlinear systems, is obtained from the long-wave approximation for arbitrary values of the exponent n. The expression for the critical viscosity is comparable to the value obtained in the numerical analysis of a discrete system with a Hertzian contact interaction (n=3/2) . The expression for p(c) in the weakly nonlinear case converges to the known equation for the critical viscosity. An initial disturbance in a discrete system approaches a stationary shock profile after traveling a short distance that is comparable to the width of the leading pulse of a stationary shock front. The shock front width is minimized when the viscosity is equal to its critical value.

Tunability of solitary wave properties in one-dimensional strongly nonlinear phononic crystals.

One-dimensional strongly nonlinear phononic crystals were assembled from chains of PTFE (polytetrafluoroethylene) and stainless-steel spheres with gauges installed inside the beads. Trains of strongly nonlinear solitary waves were excited by impacts. A significant modification of the signal shape and an increase of solitary wave speed up to two times (at the same magnitude of dynamic contact force) were achieved through a noncontact magnetically induced precompression of the chains. The data for the PTFE based chains are presented for the first time and the data for the stainless-steel beads chains are extended into a range of maximum dynamic forces more than one order of magnitude lower than previously reported. Experimental results agreed reasonably well with the long-wave approximation and numerical calculations based on the Hertz interaction law for particles interactions.

Energy trapping and shock disintegration in a composite granular medium.

We report the first experimental observation of impulse confinement and the disintegration of shock and solitary waves in one-dimensional strongly nonlinear composite granular materials. The chains consist of alternating ensembles of beads with high and low elastic moduli (more than 2 orders of magnitude difference) of different masses. The trapped energy is contained within the "softer" sections of the composite chain and is slowly released in the form of weak, separated pulses over an extended period of time. This effect is enhanced by using a specific group assembly and precompression.

Anomalous wave reflection at the interface of two strongly nonlinear granular media.

Granular materials exhibit a strongly nonlinear behavior affecting the propagation of energy and information. Dynamically self-organized strongly nonlinear solitary waves are the main information carriers in granular chains. We report the first experimental observation of the dramatic change of solitary wave reflectivity from the interface of two granular media triggered by a magnetically induced precompression. It may be appropriate to name this phenomenon the "acoustic diode" effect. We explain this effect by the high gradient of particle velocity near the interface.

Strongly nonlinear waves in a chain of Teflon beads.

One-dimensional "sonic vacuum" type phononic crystals were assembled from a chain of polytetrafluoroethylene (PTFE,Teflon) spheres with different diameters in a Teflon holder. It was demonstrated that this polymer-based sonic vacuum, with exceptionally low elastic modulus of particles, supports propagation of strongly nonlinear solitary waves with a very low speed. These solitary waves can be described using the classical nonlinear Hertz law despite the viscoelastic nature of the polymer and high strain rate deformation of the contact area. The experimentally measured speeds of solitary waves at high amplitudes are close to the theoretically estimated values with a Young's modulus of 1.46 GPa obtained from shock wave experiments. This is significantly higher than the Young's modulus of PTFE from ultrasonic measurements. Trains of strongly nonlinear solitary waves excited by an impact were investigated experimentally and were found to be in reasonable agreement with numerical calculations based on Hertz interaction law though exhibiting a significant dissipation.