It is well known that striker impact on strongly nonlinear, nondissipative, or weakly dissipative granular chains assembled from spheres (or cylinders with flat ends and spheres) having similar masses results in strongly nonlinear Nesterenko solitary waves over a very short distance from the impacted end. This paper presents the first experimental results on how the nature of the wave response, excited by striker impact on strongly nonlinear weakly dissipative discrete chains, depends on the ramp time of the incoming pulse. Variation of the pulse ramp time was accomplished using "hard" and "soft" striker impact. In the case of "hard" impact, the incoming pulse with relatively short ramp time was split into Nesterenko solitary waves after traveling about 20 particles, as in previous publications. The "soft" impact by the same striker with the same velocity was achieved by placing a small mass PTFE spherical particle inside a PTFE O-ring at the top of the first cylinder resulting in significantly longer ramp time of the incoming pulse. The incoming pulse generated by "soft" impact did not split into a train of solitary waves despite initial steepening of the wave's leading front due to strong nonlinearity. Instead, it traveled as a shocklike stress wave a long distance of 131 particles. Thus, the generation of a train of solitary waves or a shocklike stress wave in a weakly dissipative, strongly nonlinear discrete chain depends on the duration of the incoming pulse ramp. Ramping the incoming pulse resulted in a dramatic decrease in shocklike stress wave amplitude in comparison with the amplitude of the leading solitary wave in the case of "hard" impact.

It is well known that striker impact on strongly nonlinear, non-dissipative or weakly dissipative granular chains assembled from spheres (or cylinders with flat ends and spheres) having similar masses results in strongly nonlinear Nesterenko solitary waves on a very short distance from the impacted end. This paper presents the first experimental results on the nature of the wave response excited by striker impact on strongly nonlinear weakly dissipative discrete chains assembled from cylinders with flat ends and spheres having similar masses depending on the ramp time of the incoming pulse. Variation of the pulse ramp time was accomplished using "hard" and "soft" striker impact. In the case of "hard" impact, the incoming pulse with relatively short ramp time was split into Nesterenko solitary waves after traveling about 20 particles as in previous publications. The "soft" impact by the same striker with the same velocity was achieved by placing a small mass PTFE spherical particle inside a PTFE O-ring at the top of the first cylinder resulting in significantly longer ramp time of incoming pulse. The incoming pulse generated by "soft" impact did not split into a train of solitary waves despite the initial steepening of the leading front due to strong nonlinearity. Instead, it traveled as a shock-like stress wave a long distance of 131 particles. Thus, the generation of a train of solitary waves or shock-like stress wave in a weakly dissipative, strongly nonlinear discrete chain depends on the duration of the incoming pulse ramp. Ramping incoming pulse resulted in dramatic decrease of shock-like stress wave amplitude in comparison with amplitude of the leading solitary wave in case of "hard" impact.

The paper presents results of experimental and numerical research on the mechanism of macrocavity collapse in highly heterogeneous, porous mixtures of Al and W particles with large differences in strength, ductility, and density of components. Mixtures with different grain sizes of W particles and porosity were investigated in plane-strain, high-strain-rate conditions using the explosively driven thick-walled cylinder method. It was demonstrated that macroscopic axial symmetry was preserved, and a pattern of localized shear bands was not formed, which was typical for many previously investigated brittle and ductile materials. The grain size has an influence on the size of the inner cavity microscale instabilities that are formed by the flow of plastically deformed softer Al particles between W particles. Initial porosity did not significantly influence the macrocavity collapse in the investigated materials.

We study the highly nonlinear wave dynamics of 1d tensegrity metamaterials, with a focus on the interaction of a compression solitary pulse with an interface between elastically stiffening and softening materials. We observe an anomalous response of the examined system, which is characterized by the propagation of a train of reflected compression solitary waves in the stiffening branch, and the transmission of a solitary rarefaction wave with oscillatory tail in the softening branch.

The paper presents the main steps in the development of the strongly nonlinear wave dynamics of discrete systems. The initial motivation was prompted by the challenges in the design of barriers to mitigate high-amplitude compression pulses caused by impact or explosion. But this area poses a fundamental mathematical and physical problem and should be considered as a natural step in developing strongly nonlinear wave dynamics. Strong nonlinearity results in a highly tunable behaviour and allows design of systems with properties ranging from a weakly nonlinear regime, similar to the classical case of the Fermi–Pasta–Ulam lattice, or to a non-classical case of sonic vacuum. Strongly nonlinear systems support periodic waves and one of the fascinating results was a discovery of a strongly nonlinear solitary wave in sonic vacuum (a limiting case of a periodic wave) with properties very different from the Korteweg de Vries solitary wave. Shock-like oscillating and monotonous stationary stress waves can also be supported if the system is dissipative. The paper discusses the main theoretical and experimental results, focusing on travelling waves and possible future developments in the area of strongly nonlinear metamaterials. This article is part of the theme issue ‘Nonlinear energy transfer in dynamical and acoustical systems’.

The nature of short and long duration high amplitude pulses is explored in a periodic composite made of an Al matrix with W cylindrical inclusions using numerical calculations. Their wave nature is compared to the observed solitary like waves created by high amplitude short duration impact, or steady shock waves created by long duration high amplitude incoming pulses in Al-W laminates. Both composites have the same volume content of components to explore the role of mesostructure on the wave nature. The observed stress wave, in the case of short duration impact doesn't propagate as a localized solitary like wave, as was the case in the laminate. For a long duration, high amplitude loading, a shock wave is observed similar to the one propagating in the laminate.

Our motivation for this article is for students to realize that opportunities for discovery are all around them. Discoveries that can still puzzle present day researchers. Here we explore an observation by a middle school student concerning the production of what appears to be water-like “ripples” produced in aluminum foil when placed between two colliding spheres. We both applaud and explore the student’s reasoning that the ripples were formed in a melted aluminum pool.

Initiation, self-organization of shear bands, and post-critical behavior of 4340 steel with initial low (2789 MPa) and high (5420 MPa) microhardnesses, but similar thermophysical properties, are studied using the explosively-driven Thick Wall Cylinder method and numerical simulations. In experiments, low hardness 4340 steel demonstrated the initiation of a pattern of shear bands at a global effective strain of about 0.53, which did not significantly change with an increase of global strain up to 0.8. High microhardness 4340 steel demonstrated extremely different post-critical behavior. At global strain 0.56, a few well-developed shear bands propagated through the sample with their transformation into a crack pattern at larger global strain 0.83. The propagation mechanism of shear bands in hardened 4340 steel is explained by the interfacial microcracking between inclusions and matrix. The Johnson-Cook material model with damage in numerical simulations correctly predicted the dramatic change of pattern of shear bands with the change in the initial steel properties at similar global strains. The pattern of shear bands was dependent on the number of initial material defects introduced by scaling of the yield strength of mesh elements.

We present the results of measurements and numerical simulations of stress wave propagation in a one-dimensional strongly nonlinear dissipative metamaterial composed of steel disks and Nitrile O-rings. The incoming bell shape stress wave is generated by the strikers with different masses. Numerical modeling including a viscous dissipative term to describe dynamic behavior of O-rings is developed to predict the wave amplitude, shape and propagation speed of stress waves. The viscous dissipation prevented the incoming pulse from splitting into trains of solitary waves typical for non-dissipative strongly nonlinear discrete systems. The linear momentum and energy from the striker were completely transferred into this strongly nonlinear “soft” metamaterial.

We explore the role of the microstructure of AISI 4340 steel with different values of microhardness (as-received and hardened) on shear band nucleation and post-critical behavior with a well-developed pattern of shear bands. Critical and post-critical behavior was investigated with the help of the explosively-driven Thick-Walled Cylinder technique, which allowed comparative study of the material deformation at similar strain rates and final strains. It was observed that the collapsed as-received AISI 4340 samples were resilient to shear localization and propagation and mainly preserved its cylindrical geometry at the investigated small and larger global strains. The hardened specimens at the similar final global strains exhibited a dramatically different behavior. At small strains, some well-developed shear bands were observed. Larger global strains were accommodated mostly by growth of the initially generated shear bands, resulting in the complete loss of cylindrical symmetry. Numerical simulations reproduced the main features observed in the experiments and the dramatic difference in behavior of as-received and hardened AISI 4340 steel. It is shown that the initial number of defects introduced in calculations as well as the material constants used for the material model have a direct effect on the pattern of shear bands.

Explosively driven fragmentation mechanisms of Al-W particulate composite rings were investigated. The effect of mesostructures (particulate Al and W, particulate Al and W fibers) and bonding between Al particles (processing via cold isostatic and cold isostatic + hot isostatic pressing) were determined. The kinematics of the expansion process was monitored using Photon Doppler Velocimetry measurements of the velocity of the outer surface of the rings. Numerical simulations of the expansion velocity of rings were in agreement with experimental data. Agglomerated fragments larger than sizes of initial Al particles were observed in experiments. The characteristic size of these agglomerates is most likely determined by the spacing between W inclusions. The simulations show that the dynamically expanded rings had clusters of particulates between shear bands (developing into macrocracks), which expand without significant plastic deformation, generating agglomerated fragments with sizes larger than initial Al particles, as observed in experiments. It was also demonstrated that debris has a measurable fraction of particles with sizes below the original particle sizes. The mesostructure of the fragments demonstrated that Al particles were heavily deformed within the regions having locally high strain plastic flow, which may result in fragments sizes below initial Al particle diameter. Simulations agree with experiments in that Al particles between neighboring W particles/fibers are heavily plastically deformed in comparison with Al particles away from W inclusions. Simulations also demonstrated that increasing initial porosity increases the plastic straining of Al particles between W particles/fibers. Thus, initial porosity may cause an increase in temperature of the Al fragments and cracking their surface oxide layers, therefore increasing the chance of subsequent rapid oxidation in air.

We investigated numerically the nature of high amplitude stress waves generated by plate impact on Al/W viscoplastic laminates with different cell sizes. Weakly attenuating localized travelling waves, closely resembling solitary waves, quickly form near the impacted surface at relatively short duration of incoming pulse. They have properties similar to solitary solutions of the Korteweg-de Vries equation with the dispersive and nonlinear parameters connected to laminate properties. The peak temperature in the localized stress wave is dramatically different than the temperature corresponding to the shock wave at the same pressure, reflecting different paths of loading. Increase of the duration of the incoming pulse results in a train of solitary pulses or in oscillatory stationary shock like stress waves. The leading front of the shock like stress wave is closely described by the rising part of solitary stress wave.

Novel high-density aluminum (Al)-tungsten (W) fiber composites in the tubular shape with highly ordered tungsten fibers in axial and hoop directions were processed in the solid state using the combination of cold isostatic pressing and hot isostatic pressing. Half of the specimens were additionally heat treated after hot isostatic pressing to regain the properties of aluminum 6061-T6. The strength of both types of samples was investigated under quasistatic compression. Samples after additional heat treatment had the higher microhardness of matrix and compressive strength. No significant reaction between tungsten fibers and aluminum matrix was detected. The micromechanism of samples failure under compression was revealed by removing the aluminum matrix after tests with acid-etching demonstrating that tungsten fibers oriented in the axial direction were deformed by microbuckling and kinking. The sample bulging due to plastic flow of aluminum matrix resulted in the cooperative fracture of tungsten fibers in the hoop direction.

The shock waves generated by a plate impact are numerically investigated in Al-W laminates with different mesostructures. The main characteristic time scales (and the corresponding spatial scales) related to the formation of the stationary shock are identified: the duration (width) of the leading front, the time (distance) from the impact required to establish a stationary profile, and the shock front width, identified as a time span (distance) from the initial state to the final quasiequilibrium state. It is demonstrated that the width of the leading front and the maximum strain rates are determined by the dispersive and the nonlinear parameters of the laminate and not by the dissipation, as is the case for uniform solids. The characteristic spatial scale of the leading front is related to the spatial scale observed on solitarylike waves, which are satisfactorily described by the Korteweg-de Vries (KdV) approximation, as well as the speed of the wave and the ratio of maximum to final strain. The dissipation affects the width of the transition distance (shock front width) where multiple loading-unloading cycles bring the laminate into the final quasiequilibrium state. This spatial scale is of the same order of magnitude as the distance to form stationary shock wave. The period of fast decaying oscillations is well described by the KdV approach and scales linearly with the cell size. The rate of the decay of the oscillations in the numerical calculations does not scale with the square of the cell size as expected from the dissipative KdV approach that assumes a constant viscosity. This is due to the different mechanisms of dissipation in high-amplitude compression pulses.

The split Hopkinson pressure bar was used to investigate the dynamic behavior of high density aluminum alloy (Al 6061-T6) - tungsten (W) fibers composite tubes with periodic arrangements of W fibers in axial and hoop directions processed by using the combination of Cold Isostatic Pressing (CIPing) and Hot Isostatic Pressing (HIPing). Additional heat treatment of some samples allowed them to regain the original strength of Al 6061-T6, which was annealed during HIPing. The high-strain-rate deformation resulted in the strength increase for both types of samples (with and without the heat treatment) compared to quasi-static deformation. Samples after additional heat treatment exhibited higher dynamic strength. We consider that the strain rate sensitivity of the composite samples is caused by W fibers, which are responsible for the high strength of the samples and mechanism of their fracture.After dynamic tests, the Al matrix was chemically removed from the heavily deformed samples to reveal the mode of deformation of the W fibers: microbuckling and kinking in the axial direction. These mechanisms initiated the fracture of the composite samples followed by sample bulging due to plastic flow of the Al matrix and the subsequent fracture of W fibers in the hoop direction. (C) 2016 Elsevier Ltd. All rights reserved.

We study the evolution of high-amplitude stress pulses in periodic dissipative laminates taking into account the nonlinear constitutive equations of the components and their dissipative behavior. Aluminum-tungsten laminate was selected due to the large difference in acoustic impedances of components, the significant nonlinearity of the aluminum constitutive equation at the investigated range of stresses, and its possible practical applications. Laminates with different cell size, which controls the internal time scale, impacted by plates with different thicknesses that determine the incoming pulse duration, were investigated. It has been observed that the ratio of the duration of the incoming pulse to the internal characteristic time determines the nature of the high-amplitude dissipative propagating waves-a triangular oscillatory shock-like profile, a train of localized pulses, or a single localized pulse. These localized quasistationary waves resemble solitary waves even in the presence of dissipation: The similar pulses emerged from different initial conditions, indicating that they are inherent properties of the corresponding laminates; their characteristic length scale is determined by the scale of mesostructure, nonlinear properties of materials, and the stress amplitude; and a linear relationship exists between their speed and amplitude. They mostly recover their shapes after collision with phase shift. A theoretical description approximating the shape, length scale, and speed of these high-amplitude dissipative pulses was proposed based on the Korteweg-de Vries equation with a dispersive term determined by the mesostructure and a nonlinear term derived using Hugoniot curves of components.

The paper presents results on the mechanisms of plastic strain accommodation of Ni-Al laminates composed of concentrically aligned thin foils processed at different conditions undergoing a high strain radial collapse in thick walled cylinder experiments. Numerical simulations were conducted to examine the influence of mesoscale parameters (layer size, defects in mesostructure, and ductility) on the mechanisms of large plastic strain accommodation (high amplitude cooperative buckling; high frequency, low amplitude buckling; and kinking) at high strain rates in pure shear (plane strain) conditions. These mechanisms are dramatically different than observed in solid ductile and brittle homogeneous materials where a pattern of shear bands is the major mode of strain accommodation. It was observed that the layer thickness and ductility greatly influenced the dominant mode of plastic strain accommodation. The number of apices was related to the layer thickness. The presence of defects mainly had a localized area of influence. Numerical simulations showed good qualitative agreement with the experiments and provided the ability to simulate additional mesoscale and material dependencies: the role of friction/bonding, relative layer sizes, and sample thickness.

This paper focuses on the multiscale mechanism of collapse of hemicylindrical annular surface macrocavities in steel caused by high-strain, high-strain rate plastic flow of copper. Experiments and simulations revealed that a two-stage process is responsible for the observed microjetting phenomena: the formation of lateral copper microjets from the localized shear flow in copper at the interface during the filling of the cavity, and their subsequent collision at the apex of the macrocavity generating two additional horizontal microjets. The lengths of these microjets were an order of magnitude smaller than the cavity size but linearly scaled with the cavity radius. This process of microjet development is sensitive to the cavity geometry and is unlike the previously observed jetting phenomena in cavitation, impact crater collapse, or shock-induced cavity collapse.

Attenuation of short stress pulses under different levels of precompression was investigated in a one-dimensional strongly nonlinear discrete metamaterial assembled using alternating steel disks and toroidal Nitrile O-rings. The results were compared with the numerical modeling. A double power-law is used to describe the nonlinear interaction between the disks due to the compression of rubber O-rings. The dispersion behavior caused by the periodic arrangement of elements is contributing to the attenuation of pulse, but could not explain the experimental observations. It was explained by taking into account the nonlinear viscous behavior of O-rings. The numerical simulations were able to predict the dependence of the signal speed on the precompression force, a significant decrease of the pulse width with the precompression and the attenuation of the leading positive pulse, the latter of major significance in the protection against impact. This strongly nonlinear dissipative metamaterial has a potential for attenuation of dynamic loading and allows an enhanced tunability of signal speed and degree of attenuation.