Propagation of Rarefaction Pulses in Discrete Materials with Strain-Softening Behavior

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 $F \propto \delta^{n}$, 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.Comment: 15 pages, 4 figure

Highly nonlinear solitary waves in periodic dimer granular chains

We investigate 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 and heavier beads (stainless steel) are alternated with softer and lighter ones (polytetrafluoroethylene beads). We find good 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 into the influence of the dimer lattice on the properties (width and propagation speed) of the highly nonlinear wave solutions

A Monte Carlo packing algorithm for poly-ellipsoids and its comparison with packing generation using Discrete Element Model

Granular material is showing very often in geotechnical engineering, petroleum engineering, material science and physics. The packings of the granular material play a very important role in their mechanical behaviors, such as stress-strain response, stability, permeability and so on. Although packing is such an important research topic that its generation has been attracted lots of attentions for a long time in theoretical, experimental, and numerical aspects, packing of granular material is still a difficult and active research topic, especially the generation of random packing of non-spherical particles. To this end, we will generate packings of same particles with same shapes, numbers, and same size distribution using geometry method and dynamic method, separately. Specifically, we will extend one of Monte Carlo models for spheres to ellipsoids and poly-ellipsoids

Highly nonlinear solitary waves in heterogeneous periodic granular media

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, brass, 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 good agreement between experiments and numerical simulations. We also find 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

Optimization of the dynamic behavior of strongly nonlinear heterogeneous materials

New aspects of strongly nonlinear wave and structural phenomena in granular media are developed numerically, theoretically and experimentally. One-dimensional chains of particles and compressed powder composites are the two main types of materials considered here. Typical granular assemblies consist of linearly elastic spheres or layers of masses and effective nonlinear springs in one- dimensional columns for dynamic testing. These materials are highly sensitive to initial and boundary conditions, making them useful for acoustic and shock-mitigating applications. One-dimensional assemblies of spherical particles are examples of strongly nonlinear systems with unique properties. For example, if initially uncompressed, these materials have a sound speed equal to zero ("sonic vacuum"), supporting strongly nonlinear compression solitary waves with a finite width. Different types of assembled metamaterials will be presented with a discussion of the material's response to static compression. The 'acoustic diode effect' will be presented, which may be useful in shock mitigation applications. Systems with controlled dissipation will also be discussed from an experimental and theoretical standpoint emphasizing the critical viscosity that defines the transition from an oscillatory to monotonous shock profile. The dynamic compression of compressed powder composites may lead to self-organizing mesoscale structures in two and three dimensions. A reactive granular material composed of a compressed mixture of polytetrafluoroethylene (PTFE), tungsten (W) and aluminum (Al) fine-grain powders exhibit this behavior. Quasistatic, Hopkinson bar, and drop-weight experiments show that composite materials with a high porosity and fine metallic particles exhibit a higher strength than less porous mixtures with larger particles, given the same mass fraction of constituents. A two-dimensional Eulerian hydrocode is implemented to investigate the mechanical deformation and failure of the compressed powder samples in simulated drop-weight tests. The calculations indicate that the dynamic formation of mesoscale force chains increase the strength of the sample. This is also apparent in three-dimensional finite element calculations of drop- weight test simulations using LS-Dyna despite a higher granular bulk coordination number, and an increased mobility of individual grain

Quantifying the hierarchy of structural and mechanical length scales in granular systems

Continuum modeling of granular media is made possible by the existence of a length scale at and above which grain-resolved properties can be meaningfully homogenized. Progress has been made in identifying such length scales relevant to local structural properties such as porosity. However, a systematic analysis of scales above which different mechanical properties can be homogenized has yet to emerge. Here, X-ray tomography and 3D X-ray diffraction data are examined to identify such length scales. The data was obtained in-situ in compressed granular materials with rigid and flexible confinement. The experimental data are supplemented with validated discrete element simulations which examine different system sizes and different boundary conditions. Our study reveals a hierarchy in the length scales of granular solids, with lengths governing structural variables being the shortest, lengths of stress variables being intermediate, and lengths of energy dissipation being the longest. All structural and mechanical length scales obey a power law based on the theory of Geostatistics, implying that the length scales can be found by analyzing samples significantly smaller than the length scales themselves. The length scales are also found to be sensitive to boundary conditions, implying that they are extrinsic features of granular media

Quantifying local rearrangements in three-dimensional granular materials : Rearrangement measures, correlations, and relationship to stresses

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