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Quantifying the ways in which local particle rearrangements contribute to macroscopic plasticity is one of the fundamental pursuits of granular mechanics and soft matter physics. Here we examine local rearrangements that occur naturally during the deformation of three samples of 3D granular materials subjected to distinct boundary conditions by employing in situ x-ray measurements of particle-resolved structure and stress. We focus on five distinct rearrangement measures, their statistics, interrelationships, contributions to macroscopic deformation, repeatability, and dependence on local structure and stress. Our most significant findings are that local rearrangements (1) are correlated on a scale of three to four particle diameters, (2) exhibit volumetric strain-shear strain and nonaffine displacement-rotation coupling, (3) exhibit correlations that suggest either rearrangement repeatability or that rearrangements span multiple steps of incremental sample strain, and (4) show little dependence on local stress but correlate with quantities describing local structure, such as porosity. Our results are presented in the context of relevant plasticity theories and are consistent with recent findings suggesting that local structure may play at least as important of a role as local stress in determining the nature of local rearrangements.

We present new in-situ measurements of particle rotations and energy dissipation during compression of 3D packings of stiff, frictional particles. Two confined, uniaxial compression tests with different degrees of lateral confinement are discussed. X-ray computed tomography and 3D X-ray diffraction were combined to provide inter-particle forces, slip and roll distances, twist angles, and energy dissipation at all inter-particle contacts. Each of these measured quantities followed exponential distributions above their respective mean values and power-law distributions below their mean values in both experiments. Changes in these distributions during experiments suggest that the quantities generally became more homogeneous with increasing overall sample stress. Contact roll and slip distances, twist angles, and energy dissipation were all more heterogeneous than inter-particle normal force magnitudes in both experiments. Energy dissipation due to inter-particle slipping accounted for 95% of the total energy dissipated in both experiments. Dissipation mechanisms at inter-particle contacts bearing more than the mean normal force were responsible for approximately 70% of each sample’s dissipated energy at each load step, even though these contacts constituted approximately 40% of the total number of contacts.

Pressure–density relationships derived from the experimentally obtained shock and particle velocities are critical to define a material’s equation of state (EOS). Typically, impact experiments coupled with velocimetry are used to map a material’s Hugoniot. Limitations such as sample geometry and varying indices of refraction may prevent proper characterization using traditional techniques such as photon doppler velocimetry (PDV) or velocity interferometer system for any reflector (VISAR). Here, traditional Hugoniot measurements using PDV are compared to dynamic x-ray imaging encompassing two different sample geometries on the gas gun platform. Through each of these methods an experimentally derived Hugoniot is determined for a previously uncharacterized polymeric material, Somos Watershed XC11122, that is used 3D printed stereolithography parts. A Us–up relationship was determined to be Us = 2.93 us + 1.73 mm/μs through traditional PDV. Slope and sound speed values determined from x-ray imaging methods varied 11% from PDV measurements. Each method yielded a Hugoniot with densities similar to poly(methyl methacrylate) (PMMA). The similarity shows the viability of such analyses for dynamic properties and Hugoniot data. The performance and analysis of both PDV and dynamic x-ray measurements are laid out in this work. Comparing PDV and x-ray imaging highlights distinct advantages and disadvantages among each method. PDV provides less uncertainty for velocity measurements, however x-ray imaging is more spatially resolved allowing for shock steadiness observations of value when studying heterogeneous materials. Additionally, x-ray imaging provides greater insight into the shape and heterogeneity of the shock front as well as uniaxial strain state (1D zone) assumptions.

The existence of a deep borehole in the Earth’s crust disturbs the local stresses and creates a stress concentration that may result in breakout and damage to the borehole. Maintaining wellbore integrity mitigates environmental impacts such as groundwater contamination, gas leakage to the atmosphere, and fluid spills and seepage at the surface. In this paper, the stability of deep boreholes (5 km) is examined by laboratory experiments and numerical models in the context of nuclear waste disposal in Israel. Two rock types in southern Israel are considered: the crystalline basement (granite) and the Zenifim Formation (arkose). A series of room-temperature triaxial rock deformation experiments were conducted at different confining pressures. This mechanical characterization was then used to parameterize the elastic properties and damage behavior of the rocks. This facilitated modeling the stability of the deep boreholes by two different formulations of damage rheology: a dynamic-oriented formulation used to model deformation immediately after the creation of the open hole and a quasi-static formulation used to model longer stress corrosion regime. The calibrated modeling results indicate greater stability with Zenifim arkose than the crystalline granite for deep borehole conditions despite the granite having a greater triaxial compressive strength. Dissipation associated with dilation and porous compaction in the arkose during deformation plays a significant stabilizing role in the borehole compared to crystalline rocks. These results suggest that common strength-based borehole stability assessment may lead to inaccurate predictions. Three-dimensional modeling of bottom-hole stress conditions and the effects of transient borehole geometry show conventional two-dimensional analysis may not be conservative when predicting borehole damage.

Significance Structure-property relations of granular materials are governed by the arrangement of particles and the chains of forces between them. These relations enable design of wave damping materials and nondestructive testing technologies. Wave transmission in granular materials has been extensively studied and demonstrates rich features: power-law velocity scaling, dispersion, and attenuation. However, the precise roles of particle arrangements and force chains on these features remain topics of continued research interest. Here, we employ X-ray measurements and analyses to show that velocity scaling and dispersion arise from both particle arrangements and force chains, while attenuation arises mainly from particle arrangements., Ultrasound propagation through externally stressed, disordered granular materials was experimentally and numerically investigated. Experiments employed piezoelectric transducers to excite and detect longitudinal ultrasound waves of various frequencies traveling through randomly packed sapphire spheres subjected to uniaxial compression. The experiments featured in situ X-ray tomography and diffraction measurements of contact fabric, particle kinematics, average per-particle stress tensors, and interparticle forces. The experimentally measured packing configuration and inferred interparticle forces at different sample stresses were used to construct spring networks characterized by Hessian and damping matrices. The ultrasound responses of these network were simulated to investigate the origins of wave velocity, acoustic paths, dispersion, and attenuation. Results revealed that both packing structure and interparticle force heterogeneity played an important role in controlling wave velocity and dispersion, while packing structure alone quantitatively explained most of the observed wave attenuation. This research provides insight into time- and frequency-domain features of wave propagation in randomly packed granular materials, shedding light on the fundamental mechanisms controlling wave velocities, dispersion, and attenuation in such systems.

The penetration depth of a projectile is determined by the strength and deformation behavior of the granular material into which it impacts, which is affected by fracture of individual grains within the granular assembly. Interparticle forces, leading to contact stresses and ultimately fracture initiation, are influenced by particle morphology. A numerical method that incorporates both particle fracture and morphology can provide a more accurate model of projectile penetration. In this research, a numerical approach utilizing high resolution x-ray computed tomography (CT) to incorporate grain morphology and an explicit finite element code which includes damage mechanics for simulating grain fracture is used to analyze an assembly of Ottawa sand particles subjected to a one-dimensional confined compression loading, simulating the high stresses present at the tip of the projectile as it penetrates the ground. A small granular assembly of CT imaged Ottawa sand particles is analyzed with and without incorporating damage mechanics to investigate the initiation of particle fracture and its effect on the projectile's depth. This approach can then be used to create multi-scale models of granular assemblies under projectile loading considering the effect of individual particle shape and fracture on the penetration response through well calibrated numerical simulations.

Three-dimensional X-ray diffraction and X-ray computed tomography are used to study the grain-scale response of angular granular materials to understand grain kinematics, stresses and rotations during compaction and to compare the responses of angular grains with those of spherical grains., Three-dimensional X-ray diffraction (3DXRD), a method for quantifying the position, orientation and elastic strain of large ensembles of single crystals, has recently emerged as an important tool for studying the mechanical response of granular materials during compaction. Applications have demonstrated the utility of 3DXRD and X-ray computed tomography (XRCT) for assessing strains, particle stresses and orientations, inter-particle contacts and forces, particle fracture mechanics, and porosity evolution in situ. Although past studies employing 3DXRD and XRCT have elucidated the mechanics of spherical particle packings and angular particle packings with a small number of particles, there has been limited effort to date in studying angular particle packings with a large number of particles and in comparing the mechanics of these packings with those composed of a large number of spherical particles. Therefore, the focus of the present paper is on the mechanics of several hundred angular particles during compaction using in situ 3DXRD to study the crystal structure, kinematics, stresses and rotations of angular quartz grains. Comparisons are also made between the compaction response of angular grains and that of spherical grains, and stress-induced twinning within individual grains is discussed.

Grain fracture and crushing are known to influence the macroscopic mechanical behavior of granular materials and be influenced by factors such as grain composition, morphology, and microstructure. In this paper, we investigate grain fracture and crushing by combining synchrotron x-ray computed tomography and three-dimensional x-ray diffraction to study two granular samples undergoing uniaxial compaction. Our measurements provide details of grain kinematics, contacts, average intra-granular stresses, inter-particle forces, and intra-grain crystal and fracture plane orientations. Our analyses elucidate the complex nature of fracture and crushing, showing that: (1) the average stress states of grains prior to fracture vary widely in their relation to global and local trends; (2) fractured grains experience inter-particle forces and stored energies that are statistically higher than intact grains prior to fracture; (3) fracture plane orientations are primarily controlled by average intra-granular stress and contact fabric rather than the orientation of the crystal lattice; (4) the creation of new surfaces during fracture accounts for a very small portion of the energy dissipated during compaction; (5) mixing brittle and ductile grain materials alters the grain-scale fracture response. The results highlight an application of combined x-ray measurements for non-destructive in situ analysis of granular solids and provide details about grain fracture that have important implications for theory and modeling.

The paper describes a novel computational approach to refine continuum models for penetration calculations which involves two stages. At the first stage, a trial continuum model is used to model penetration into a concrete target. Model parameters are chosen to match experimental data on penetration depth. Deformation histories are recorded at few locations in the target around the penetrator. In the second stage, these histories are applied to the boundaries of a representative volume comparable to the element size in large scale penetration simulation. Discrete-continuum approach is used to model the deformation and failure of the material within the representative volume. The same deformation histories are applied to a single element which uses the model to be improved. Continuum model may include multiple parameters or functions which cannot be easily found using experimental data. We propose using mesoscale response to constrain such parameters and functions. Such tuning of the continuum model using typical deformation histories experienced by the target material during the penetration allows us to minimize the parameter space and build better models for penetration problems which are based on physics of penetration rather than intuition and ad hoc assumptions.

Numerical modeling of unconsolidated granular materials is comprised of multiple nonlinear phenomena. Accurately capturing these phenomena, including intergranular forces and grain deformation, depends on resolving contact regions several orders of magnitude smaller than the grain size. Here, we investigate a method for capturing the morphology of the individual particles using computed X-ray tomography, which allows for accurate characterization of the interaction between grains. Additionally, the ability of these numerical approaches to determine stress concentrations at grain contacts is important in order to capture catastrophic splitting of individual grains, which has been shown to play a key role in the plastic behavior of the granular material on the continuum level. Samples of Ottawa sand are numerically modeled under one-dimensional compression loadings in order to determine the effect of discretization approaches, such as mesh refinement, on the resulting stress concentrations at contact points between grains. The effects of grain coordination number and finite element type selection on these stress concentrations are also investigated.

The objective of this paper is to develop an analytical expression for temperature in a thermodynamically consistent model with a Mie-Gruneisen equation for pressure. This expression for the temperature is obtained for both constant and variable specific heat models and can be used in common models for the material yield strength that include thermal softening due to increase in temperature. Also, the material parameters in the model can easily be calibrated to match known experimental data and the model has been used to determine the value of the shock pressure at the onset of melting during shock loading.

Dynamic compression of composite materials is of scientific interest because the mechanical mismatch between internal phases challenges continuum theories. Typical assumptions about steady wave propagation and quasi-instantaneous state changes require reexamination along with the need for time-dependent models. To that end, data and models are presented for the shock compression of an idealized particulate composite. To serve as a generic representative of this material class, a polymer matrix was filled with tungsten particles, ranging from 1 to 50 vol. %. This creates a simple microstructure containing randomly scattered particles with an extreme impedance mismatch to the binding matrix. These materials were parallel plate impact loaded by Al flyers traveling at 1.8–5.0 km/s. Velocimetry provided records of the equilibrium state and the compression wave structure for each case with trends quantified by an empirical fit. The same quantities were also studied as a function of the wave's propagation distance. A homogenized viscoelastic model then made it possible to progress from cataloging trends to making predictions. Starting from a Mie–Gruneisen equation of state, additional time varying terms were added to capture the transient response. After calibration, accurate predictions of the steady wave structure were possible.

Heterogeneous materials do not respond mechanically to an impulse in the manner of homogeneous metals and alloys. Wave propagation in a microstructure with chemically distinct identities, that are only in incidental contact with each other, is a complex process and not well understood. Here we report on a series of plate-impact experiments on a polymer-metal composite, where the volume fraction of the metallic phase was systematically varied from 0% to 40%, while other parameters like the sample thickness were kept constant. The velocity histories at the sample/window interfaces were measured to examine the continuum response corresponding to the internal materials processes. The unfilled polymer demonstrated a steady shock wave response; whereas the wave profiles obtained from mixture samples showed structured waves that depended on the volume fraction of the fill. The shock wave profiles were quantified using parameters strongly correlated to the material composition. The likely physical basis of these correlations is discussed.

Accurately describing the dynamic compaction of granular materials is a persistent challenge in computational mechanics. Using a synchrotron x-ray source we have obtained detailed imaging of the ev...

The response of particulate materials to impulsive loading includes complex interactions between grains due to fracture and comminution and the presence of interstitial material. The quasi-static strength of saturated powders is related to the concept of “effective stress” in which the fluid stiffens the material response and reduces the shear strength. However, detailed information regarding the effects of saturation under dynamic loading is lacking since static equilibrium between phases cannot be assumed and the interaction becomes more complex. Recent experiments on the IMPULSE (IMPact System for ULtrafast Synchrotron Experiments) capability at the Dynamic Compression Sector (DCS) of the Advanced Photon Source (APS) have captured in-situ X-ray phase-contrast images of shock loaded soda lime glass spheres in dry and saturated conditions. Previous investigations have observed reduction of fragmentation attributed to “cushioning” of an interstitial fluid in impact recovery experiments. The differences between the modes of deformation and compaction are compared with direct numerical simulations showing that the cause of fracture is different. In drained (dry) impact experiments at 300 m/s, the fractures initiate near the contact point between grains. In fully saturated experiments with identical impact conditions, spallation is observed during the incident stress-wave passage in the glass before the H2O has equilibrated.

We propose a weighted Nitsche framework for small-sliding frictional contact problems on three-dimensional interfaces. The proposed method inherits the advantages of both augmented Lagrange multiplier and penalty methods while also addressing their shortcomings. Algorithmic details of the traction update and consistent linearization in the presence of Nitsche terms are provided. Several benchmark numerical experiments are conducted and the results are compared with existing studies. The results are encouraging and indicate accurate satisfaction of the non-interpenetration constraint, stable tractions and asymptotic quadratic convergence of the Newton–Raphson method.

Assessments of asteroid deflection strategies depend on material characterization to reduce the uncertainty in predictions of the deflection velocity resulting from impulsive loading. In addition to strength, equation of state, the initial state of the material including its competency (i.e. fractured or monolithic) and the amount of micro- or macroscopic porosity are important considerations to predict the thermomechanical response. There is recent interest in observing near-Earth asteroid (101955) Bennu due to its classification of being potentially hazardous with close approaches occurring every 6 years. Bennu is relatively large with a nominal diameter of 492 m, density estimates ranging from 0.9-1.26 g/cm 3 and is composed mainly of carbonaceous chondrite. There is a lack of data for highly porous carbonaceous chondrite at very large pressures and temperatures. In the absence of the specific material composition and state (e.g. layering, porosity as a function of depth) on Bennu we introduce a continuum constitutive model based on the response of granular materials and provide impact and standoff explosion simulations to investigate the response of highly porous materials to these types of impulsive loading scenarios. Simulations with impact speeds of 5 km/s show that the shock wave emanating from the impact site is highly dispersive and that a 10% porous material has a larger compacted volume compared with a 40% porous material with the same bulk density due to differences in compaction response. A three-dimensional simulation of a 190 kT standoff explosion 160 m off the surface of a shape model of Bennu estimated a deflection velocity of 10 cm/s.

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.

The dynamic compaction of initially porous material is typically treated in continuum dynamics simulations via adjustments to the scalar equation of state (EOS) of the bulk, porous material relative to that of the solid. However, the behavior during compaction is governed by inelastic processes, as the solid material deforms, largely by shearing, to fill the voids. The resulting response depends on the strain path, e.g. isotropic versus uniaxial loading. Adjustments to the EOS are therefore fundamentally unsuited to describing porous compaction, and it is desirable to consider porous effects through the stress and strain tensors. We have performed mesoscale simulations, resolving the microstructure explicitly, to guide the construction of continuum models. These simulations allow us to study the interplay between strength and EOS in the solid, the extent of dissipative flow versus non-dissipative displacement, and the evolution of porosity and micro-morphological features.

Fracture of individual grains within a granular assembly affect the strength and deformation behavior of granular materials under large stress states. Interparticle forces, leading to contact stresses and ultimately fracture initiation, are influenced by particle morphology. A numerical method that incorporates both particle fracture and morphology can provide a more accurate model of a granular material’s macro-scale response. This research investigates an approach to modeling fracture initiation and propagation within individual grains, utilizing high resolution X-ray computed tomography (CT) imaging to consider grain morphology and an explicit finite element code optimized for high performance computing which incorporates damage mechanics. Using precisely measured force-displacement curves from single particle crushing tests of manufactured quartz spheres, the method is validated, and the effects of fracture properties on grain fragmentation are determined. This approach is then used to simulate single particle crushing of Ottawa sand, with grain morphology incorporated through discretized CT images. The effect of grain orientation on the force and applied displacement at catastrophic splitting is also explored. The proposed discrete particle based finite element framework can be applied to modeling granular assemblies, considering the effect of individual particle shape and fracture on the assembly’s deformation response through well calibrated numerical simulations.

Dynamic compaction of granular materials is a complex process, wherein the material response at the continuum scale arises from fracture, comminution, and fragment flow at the grain scale. Granular materials have heterogeneity due to variation in grain properties as well as variation in local packing density and structure. These heterogeneities may affect the dynamic compaction response, producing a structured and time-varying compaction front. The methodology used to characterize the shock behavior in solid materials may be inappropriate for granular materials because of this unsteady behavior and interactions between the granular material and measurement surfaces. To observe the compaction front heterogeneity, in situ x-ray imaging of granular compaction is conducted at a scale between the grain- and continuum scales. To allow for sufficient x-ray transmission, a thin sample geometry is used, for which boundary affects may result in a significantly different load path than would occur in a 1-D compaction configuration. Numerical simulations of the experimental geometry support the analysis of the results so that the feature of the compaction front can be distinguished from artifacts of the experimental configuration. The results suggest that compaction front heterogeneity may have structure with a length scale of tens of particle diameters and demonstrate that finite grain size can inhibit the formation of shear-induced features that would arise in a homogenized representation of the same material.

The National Academy has recently produced reports on the potential hazard and mitigation strategies for near Earth objects (NEO) [1] , [2] . The NRC reported to Congress that nuclear explosives are the only current technology to protect the Earth from impact of large asteroids. This is mainly due to difficulties in predicting the impact with high confidence leading to a short time to impact. Thus, the velocity deflection required when they are determined to be potentially hazardous asteroids (PHA) can only be achieved with nuclear explosives. A standoff explosion, without direct contact with the Near Earth Object (NEO) is a robust option for a non-destructive push, which offers several advantages. We have investigated the efficiency of energy deposition and its dependence on porosity and strength properties of NEO. An Eulerian hydrocode (GEODYN) with an interface reconstruction algorithm, wide-range equation of states and a flexible constitutive model library was used for numerical studies. The largest difficulties in predicting deflection velocity and fragmentation of asteroids are related to uncertainty in composition and mechanical properties of NEO. To reduce this uncertainty, we performed simulations of normal impact cratering of an NEO surface and related results with observables such as the crater shapes, the critical crater diameter (necessary to remove previous craters) and the maximum crater size (necessary for asteroid break-up). The velocity distribution of the material ejected from the impact crater is also germane to the asteroid deflection problem where the ablated material provides the thrust resulting in a deflection velocity. We performed parametric studies on how porosity and strength of the asteroid would affect these results.

We use experiments, numerical simulations, and theoretical analysis to investigate the propagation of highly nonlinear solitary waves in periodic arrangements of dimer (two-mass) and trimer (three-mass) cell structures in one-dimensional granular lattices. To vary the composition of the fundamental periodic units in the granular chains, we utilize beads of different materials (stainless steel, bronze, glass, nylon, polytetrafluoroethylene, and rubber). This selection allows us to tailor the response of the system based on the masses, Poisson ratios, and elastic moduli of the components. For example, we examine dimer configurations with two types of heavy particles, two types of light particles, and alternating light and heavy particles. Employing a model with Hertzian interactions between adjacent beads, we find very good agreement between experiments and numerical simulations. We find equally good agreement between these results and a theoretical analysis of the model in the long-wavelength regime that we derive for heterogeneous environments (dimer chains) and general bead interactions. Our analysis encompasses previously-studied examples as special cases and also provides key insights on the influence of heterogeneous lattices on the properties (width and propagation speed) of the nonlinear wave solutions of this system., 17 pages, 2 tables, 12 figures (several with multiple panels)

Ball-milling Al-metal powders can result in self-sustaining high-temperature synthesis in intermetallic-forming systems. Here, Al and Ni powders with similar composition are used to investigate how microstructural differences affect the measured time to reaction (TTR) between powders of different sizes processed under milling conditions specified by statistically designed experiments. Linear statistical models predicting the TTR and the change in temperature (Δ T ) are built from these experimental results. The time required to observe a self-sustained high-temperature synthesis of NiAl with different combinations of the powders and ball-milling conditions vary by almost an order of magnitude. Comparisons of powders milled to times corresponding to percentages of their averaged TTR show similar reaction initiation temperatures despite the difference in total milling time. Several distinct arrested reactions within the powder grains exhibit rapid solidification or incomplete diffusion of Ni into Al, forming porous Ni-rich layered structures. The partially reacted grains suggest that the composite laminate particles are not forming intermetallic on the grain scale, but on the localized scale between layers.

Strongly nonlinear periodic waves are investigated in an initially compressed chain of spheres under Hertz contact. A harmonic excitation force disturbs the first grain with an amplitude comparable to the initial compression and the steady strain-wave profiles at large distances from this disturbance are compared with predictions from the long wave approximation. Two qualitatively different types of quasi-stationary periodic waves are apparent in the system: one with minimum and maximum strain values above the static value and one whose minimum strain is below and maximum value is above the initial strain. From the frequency spectrums of the calculated force between particles, new forcing functions are constructed that allow rapid formation of quasi-stationary strongly nonlinear periodic waves.

This document serves as a final report to a small effort where several improvements were added to a LLNL code GEODYN-­L to develop Discrete Element Method (DEM) algorithms coupled to Lagrangian Finite Element (FE) solvers to investigate powder-­bed formation problems for additive manufacturing. The results from these simulations will be assessed for inclusion as the initial conditions for Direct Metal Laser Sintering (DMLS) simulations performed with ALE3D. The algorithms were written and performed on parallel computing platforms at LLNL. The total funding level was 3-­4 weeks of an FTE split amongst two staff scientists and one post-­doc. The DEM simulations emulated, as much as was feasible, the physical process of depositing a new layer of powder over a bed of existing powder. The DEM simulations utilized truncated size distributions spanning realistic size ranges with a size distribution profile consistent with realistic sample set. A minimum simulation sample size on the order of 40-­particles square by 10-­particles deep was utilized in these scoping studies in order to evaluate the potential effects of size segregation variation with distance displaced in front of a screed blade. A reasonable method for evaluating the problem was developed and validated. Several simulations were performed to showmore » the viability of the approach. Future investigations will focus on running various simulations investigating powder particle sizing and screen geometries.« less

The strongly nonlinear interaction between elements in discrete materials (e.g., grains in granular media) is responsible for their unique wave propagation properties. The paper will present an experimental observation of impulse energy confinement and the resultant disintegration of shock and solitary waves by discrete materials with strongly nonlinear interaction between elements. Experiments and numerical calculations will be presented for alternating ensembles of high-modulus vs orders of magnitude lower-modulus chains of spheres of different masses. The trapped energy is contained within the “softer” portions 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 a superimposed force.

This article details some of the techniques used to derive exact solutions from the discrete equations of motion of strongly and weakly nonlinear discrete systems. The distinction between strongly and weakly nonlinear systems is related to the amplitude of a traveling pulse and the external confining load. Materials with an anomalous strain-softening behavior will be emphasized (i.e., [Formula: see text], [Formula: see text]), though this choice does not preclude applications for strain-hardening systems like those with Hertzian potentials. Discrete materials with tunable acoustic transmission properties and novel impact mitigation capacity have gained interest in recent years due to their practical application across many scientific fields. Wave-guides comprised of discrete materials with a nonlinear interaction potential have been used to investigate the interplay between nonlinearity, dispersion and dissipation.

Polymer-matrix particulate composites consist of individual particles of more than one material dispersed throughout and held together by a polymer binder. The mechanical and physical properties of the composite depend on the mechanical and physical properties of the individual components, particularly the polymer binder; their loading density; the shape and size of the particles; the interfacial adhesion; residual stresses; and matrix porosity. Systematic studies of the effects of volume fraction and microstructure on the behavior of these polymer-based composites are critical. The behavior of polymer-matrix particulate composites at intermediate to high strain rates has not been investigated in detail in the literature. The testing strain rate can greatly affect the behavior of these composites due to the dependency on rate dependant phase changes in the polymer binder. The intermediate strain rate behavior (~103–104/s) is studied using a split Hopkinson pressure bar. Shock, or high strain rate, properties of these composite materials have been investigated using gas gun and explosive loading techniques. This chapter will review results from recent experimental studies on the properties of polymer-based particulate composites containing metal and metal oxide powders.

One of the requisite processes for chemical reactions between solid powder particles resulting from shock loading is that the particles undergo large deformations, exposing new surfaces while mixing with surrounding material. Reactions under shock loading occur in a reaction zone, the extent of which is defined by the interfacial surface area and the depth of the diffusion layer. The former depends on the level of hydrodynamic mixing of heterogeneous material under shock, while the latter depends on temperaturedependent species diffusion. To investigate diffusion-limited reactions at the grain scale level, mass diffusion and simple reaction kinetics depending on the interfacial surface area have been implemented in an Eulerian hydrocode GEODYN. Diffusion-reaction processes that are initiated by rapid heating of a Ni/Al nanolaminate and by shock loading of a micron-scale Ni/Al powder mixture are considered.

We investigate rarefaction waves in nonlinear periodic systems with a 'softening' power-law relationship between force and displacement to understand the dynamic behavior of this class of materials. A closed form expression describing the shape of the strongly nonlinear rarefaction wave is exact for n = 1/2 and agrees well with the shape and width of the pulses resulting from discrete simulations. A chain of particles under impact was shown to propagate a rarefaction pulse as the leading pulse in initially compressive impulsive loading in the absence of dissipation. Compression pulses generated by impact quickly disintegrated into a leading rarefaction solitary wave followed by an oscillatory train. Such behavior is favorable for metamaterials design of shock absorption layers as well as tunable information transmission lines for scrambling of acoustic information.

We developed experimental set up that allowed the investigation of propagation of oscillating waves generated at the entrance of nonlinear and strongly nonlinear two‐mass granular chains composed of steel cylinders and steel spheres. The paper represents the first experimental data related to the propagation of these waves in nonlinear and strongly nonlinear chains. The dynamic compressive forces were detected using gauges imbedded inside particles at depths equal to 4 cells and 8 cells from the entrance gauge detecting the input signal. At these relatively short distances we were able to detect practically perfect transparency at low frequencies and cut off effects at higher frequencies for nonlinear and strongly nonlinear signals. We also observed transformation of oscillatory shocks into monotonous shocks. Numerical calculations of signal transformation by non‐dissipative granular chains demonstrated transparency of the system at low frequencies and cut off phenomenon at high frequencies in reasonable ...

Discrete materials composed of masses connected by strongly nonlinear links with anomalous behavior (reduction of elastic modulus with strain) have very interesting wave dynamics. Such links may be composed of materials exhibiting repeatable softening behavior under loading and unloading. These discrete materials will not support strongly nonlinear compression pulses due to nonlinear dispersion but may support stationary rarefaction pulses or rarefaction shock-like waves. Here we investigate rarefaction waves in nonlinear periodic systems with a general power-law relationship between force and displacement $F \propto ��^{n}$, where $0 < n < 1$. An exact solution of the long-wave approximation is found for the special case of $n = 1/2$, which agrees well with numerical results for the discrete chain. Theoretical and numerical analysis of stationary solutions are discussed for different values of $n$ in the interval $0 < n < 1$. The leading solitary rarefaction wave followed by a dispersive tail was generated by impact in numerical calculations., 15 pages, 4 figures

One-dimensional nonlinear phononic crystals have been assembled from periodic diatomic chains of stainless steel cylinders alternated with Polytetrafluoroethylene spheres. This system allows dramatic changes of behavior (from linear to strongly nonlinear) by application of compressive forces practically without changes of geometry of the system. The relevance of classical acoustic band-gap, characteristic for chain with linear interaction forces and derived from the dispersion relation of the linearized system, on the transformation of single and multiple pulses in linear, nonlinear and strongly nonlinear regimes are investigated with numerical calculations and experiments. The limiting frequencies of the acoustic band-gap for investigated system with given precompression force are within the audible frequency range (20–20,000 Hz) and can be tuned by varying the particle’s material properties, mass and initial compression. In the linear elastic chain the presence of the acoustic band-gap was apparent through fast transformation of incoming pulses within very short distances from the chain entrance. It is interesting that pulses with relatively large amplitude (nonlinear elastic chain) exhibit qualitatively similar behavior indicating relevance of the acoustic band gap also for transformation of nonlinear signals. The effects of an in situ band-gap created by a mean dynamic compression are observed in the strongly nonlinear wave regime.

Compressive dynamic strength and fracture pattern of Al‐W granular composites with an identical weight ratio of Al (23.8 wt%) and W (76.2 wt%) with different porosities, size and shape of W component were investigated at strain rates 1000–1500 l/s. Samples were fabricated by Cold Isostatic Pressing. A dynamic strength of composites with fine W particles (100 MPa) was significantly larger than the strength of composite with the coarse W particles (75 MPa) at the same porosity 26% (samples with porosity 15% with coarse W particles exhibited a higher strength of 175 MPa). Morphology of W inclusions had a strong effect on dynamic strength. Samples with W wires arranged in axial direction (diameter 100 microns) and porosity 16%) with the same volume content of components had a dynamic strength of 350 MPa. Dynamic behavior was numerically simulated using computer code Raven, demonstrating a strain hardening effect due to in situ densification which was observed experimentally for cold isostatically pressed Al and Al‐coarse W powders.

We report the propagation of highly nonlinear solitary waves in heterogeneous, periodic granular media using experiments, numerical simulations, and theoretical analysis. We examine periodic arrangements of particles in experiments in which stiffer/heavier beads (stainless steel) are alternated with softer/lighter ones (PTFE beads). We find excellent agreement between experiments and numerics in a model with Hertzian interactions between adjacent beads, which in turn agrees very well with a theoretical analysis of the model in the long-wavelength regime that we derive for heterogeneous environments and general bead interactions. Our analysis encompasses previously-studied examples as special cases and also provides key insights on the influence of the dimer lattice on the properties (width and propagation speed) of the obtained highly nonlinear wave solutions., Comment: 4.2 pages, 3 figures (each with multiple panels); adjustments in title, text, and figures; typos corrected; to appear in Physical Review E (rapid communication)

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 $(F\ensuremath{\propto}{\ensuremath{\delta}}^{n})$ 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.

One dimentional 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 an impact. A significant modification of the signal shape and an increase of solitary wave speed up to two times (at the same amplitude of dynamic contact force)were achieved through a noncontact magnetically induced precompression of the chains. Data for PTFE based chains are presented for the first time and data for stainless steel based chains were extended into a smaller range of amplitudes by more than one order of magnitude than previously reported. Experimental results were found to be in reasonable agreement with the long wave approximation and with numerical calculations based on Hertz interaction law for discrete chains., Comment: 36 pages, 7 figures

One dimensional "sonic vacuum"-type phononic crystals were assembled from chains of polytetrafluoroethylene (PTFE) beads and Parylene coated spheres with different diameters. It was demonstrated for the first time that these polymer-based granular system, with exceptionally low elastic modulus of particles, support the propagation of strongly nonlinear solitary waves with a very low speed. They can be described using classical nonlinear Hertz law despite the viscoelastic nature of the polymers and the high strain rate deformation of the contact area. Trains of strongly nonlinear solitary waves excited by an impact were investigated experimentally and were found to be in reasonable agreement with numerical calculations. Tunability of the signal shape and velocity was achieved through a non-contact magnetically induced precompression of the chains. This applied prestress allowed an increase of up to two times the solitary waves speed and significant delayed the signal splitting. Anomalous reflection at the interface of two "sonic vacua"-type systems was reported.

Granular materials exhibit a strongly nonlinear behaviour affecting the propagation of information in the medium. Dynamically self-organized strongly nonlinear solitary waves are the main information carriers in granular chains. Here we report the first experimental observation of the dramatic change of reflectivity from the interface of two granular media triggered by a noncontact magnetically induced initial precompression. It may be appropriate to name this phenomenon the "acoustic diode" effect. Based on numerical simulations, we explain this effect by the high gradient of particle velocity near the interface., 14 pages, 3 figures

One dimensional "sonic vacuum" type phononic crystals were assembled from a chain of Teflon spheres with different diameters in a Teflon holder. It was demonstrated for the first time 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., 33 pages, 6 figures

Granular materials demonstrate a strongly nonlinear behavior influencing the wave propagation in the medium. We report the first experimental observation of impulse energy confinement and the resultant disintegration of shock and solitary waves. The medium consists of alternating ensambles of high-modulus vs orders of magnitude lower modulus chains of different masses. The trapped energy is contained within the "softer" portions 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 superimposed force., Comment: 15 pages, 2 figures