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

Influence of Controlled Viscous Dissipation on the Propagation of Strongly Nonlinear Waves in Stainless Steel Based Phononic Crystals

Strongly nonlinear phononic crystals were assembled from stainless steel spheres. Single solitary waves and splitting of an initial pulse into a train of solitary waves were investigated in different viscous media using motor oil and non-aqueous glycerol to introduce a controlled viscous dissipation. Experimental results indicate that the presence of a viscous fluid dramatically altered the splitting of the initial pulse into a train of solitary waves. Numerical simulations qualitatively describe the observed phenomena only when a dissipative term based on the relative velocity between particles is introduced.Comment: 4 pages, 3 figures, conference pape

Solitary and shock waves in discrete double power-law materials

A novel strongly nonlinear laminar metamaterial supporting new types of solitary and shock waves with impact energy mitigating capabilities is presented. It consists of steel plates with intermittent polymer toroidal rings acting as strongly nonlinear springs with large allowable strain. Their force-displacement relationship is described by the addition of two power-law relationships resulting in a solitary wave speed and width depending on the amplitude. This double nonlinearity allows splitting of an initial impulse into two separate strongly nonlinear solitary wave trains. Solitary and shock waves are observed experimentally and analyzed numerically in an assembly with Teflon o-rings.Comment: 14 pages, 6 figure

Strongly Nonlinear Waves in Polymer Based Phononic Crystals

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

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

Pulse propagation in a linear and nonlinear diatomic periodic chain: effects of acoustic frequency band-gap

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

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

Pulse mitigation by a composite discrete medium

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