Connection machine simulation of ultrasonic wave propagation in materials III: The three-dimensional case

A formalism for the simulation by parallel processing of the propagation of ultrasonic pulses of arbitrary shape (i.e. not restricted to continuous waves) in complex media is presented. Recursive relationships yielding the time evolution of the displacement field are derived for both homogeneous and heterogeneous materials. In the latter case, formulas for cross-points at the intersection of up to eight different materials are obtained. A few examples of numerical results obtained with the proposed method are shown to demonstrate its applicability and efficiency. The problem of visualization of the results is also briefly discussed.     

Elastic wave propagation in nonlinear two-dimensional acoustic metamaterials

Nonlinear Dynamics - This study describes the wave propagation in a periodic lattice which is formed by a spring-mass two-dimensional structure with local Duffing nonlinear resonators. The wave...     

Dynamics and wave propagation in dilatant granular materials

The equations of motion for dilatant granular material are obtained from a Hamiltonian variational principle of local type in the conservative case. The propagation of nonlinear waves in a region with uniform state is studied by means of an asymptotic approach that has already appeared useful in an investigation on wave propagation in bubbly liquids and in fluid mixtures. When the grains are assumed to be incompressible, it is shown that the material behaves as a continuum with latent microstructure.

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Sommario Si ricavano le equazioni di moto per i materiali granulari dilatanti da un principio variazionale Hamiltoniano di tipo locale nel caso conservativo. Si studia la propagazione delle onde non lineari in una regione di stato costante per mezzo di un approccio asintotico già rivelatosi utile nello studio della propagazione di onde nei liquidi con bolle e nelle miscele di fluidi. Quando si supponga che i granuli siano incomprimibili, si dimostra che il materiale si comporta come un continuo con microstruttura latente.

     

Meshless simulation of crack propagation in multiphase materials

The material body considered in this work consists of multiphases. Digital imaging data are taken as the input to specify the configuration and composition of the specimen. Meshless method is demonstrated as a superior numerical tool to analyze crack initiation and propagation in multiphase material. A fracture criterion, based on the ratio of the opening stress over the material toughness distributed in front of the crack tip, is proposed to determine the direction of crack propagation of mixed mode fracture problem in multiphase material. Numerical results are presented and discussed.     

Symplectic analysis for elastic wave propagation in two-dimensional cellular structures

On the basis of the finite element analysis, the elastic wave propagation in cellular structures is investigated using the symplectic algorithm. The variation principle is first applied to obtain the dual variables and the wave propagation problem is then transformed into two-dimensional （2D） symplectic eigenvalue problems, where the extended Wittrick-Williams algorithm is used to ensure that no phase propagation eigenvalues are missed during computation. Three typical cellular structures, square, triangle and hexagon, are introduced to illustrate the unique feature of the symplectic algorithm in higher-frequency calculation, which is due to the conserved properties of the structure-preserving symplectic algorithm. On the basis of the dispersion relations and phase constant surface analysis, the band structure is shown to be insensitive to the material type at lower frequencies, however, much more related at higher frequencies. This paper also demonstrates how the boundary conditions adopted in the finite element modeling process and the structures＇ configurations affect the band structures. The hexagonal cells are demonstrated to be more efficient for sound insulation at higher frequencies, while the triangular cells are preferred at lower frequencies. No complete band gaps are observed for the square cells with fixed-end boundary conditions. The analysis of phase constant surfaces guides the design of 2D cellular structures where waves at certain frequencies do not propagate in specified directions. The findings from the present study will provide invaluable guidelines for the future application of cellular structures in sound insulation.     

Multi-mode wave propagation in ribbed plates. Part II: Predictions and comparisons

This paper addresses dispersion curve numerical computations for specific ribbed plates. Precisely, wave propagation in the direction parallel to the ribs is the main objective. First, analytical calculations are performed for such ribbed plates after which the results are compared to a more general numerical procedure. This procedure reuses a reduced finite element model of the ribbed plate and extracts guided multi-mode propagation parameters. Comparisons of analytical and numerical estimations show very good agreement. Finally, the experimental results obtained in the companion paper are considered. Specifically, experimental and numerical dispersion curves are compared over a wide frequency range. Close concordance is obtained allowing the dispersion curves to be fully interpreted.     

A non-equilibrium multiscale simulation of shock wave propagation

A novel non-equilibrium multiscale dynamics (NEMSD) is proposed to simulate non-equilibrium thermal–mechanical processes. The model couples coarse-grain thermodynamics with a fine scale molecular dynamics. A Distributed Nośe-Hoover Thermostat Network is used, which regulates the temperature in each coarse scale Voronoi cell according to the finite element (FE) nodal temperature. The atoms in each element-cell, namely Voronoi cell-ensemble, are assumed to be in a local equilibrium state within one coarse scale time step. The change of FE nodal temperature provides a source of random forces, which drive the system out of equilibrium. The proposed NEMSD can successfully simulate shock wave propagation in a cubic lattice.     

Experimental and computational modeling of wave propagation in granular materials

A hybrid experimental-computational study has been conducted in order to determine the propagational characteristics of mechanical waves in granular materials. The experimental investigation has used the method of dynamic photoelasticity to collect photographic data which provide information on the wave speeds, integranular contact loadings, and wave-spreading characteristics. The computational study employed the use of the distinct-element method whereby the motion of each granule in the material is modeled by rigid-body dynamics assuming each particle interaction has particular frictionless stiffness and damping forces. The experimental results provide special dynamic material constants necessary for the computational modeling, and they also provide data for comparison purposes. Results from the experimental and computational studies compare well with each other and indicate that local microstructure plays an important role in the wave propagation through such materials.     

Numerical simulations of shock wave propagation in condensed multiphase materials

We propose to find out numerical solutions of a travelling shock wave in condensed mixtures by using a direct numerical simulation. Condensed multiphase materials under shock wave conditions are mechanically characterized by a unique pressure and a unique velocity. In this study, the mixture is considered as a collection of grains separated by interface between each material: this problem of interfaces is solved by a diffuse interface method. The results will be compared to existing one-dimensional numerical models, analytical solutions and also experimental data. The volume fraction (or the phase temperature) is not measured in experiments and it is then important to verify the behaviour of a phase quantity through various methods. A non-monotonous evolution of the volume fraction is obtained with analytical solution as well as numerical simulation.      

Discrete element simulation of shock wave propagation in polycrystalline copper

The implementation of the characteristic of compressive plasticity into the Discrete Element Code, DM2, while maintaining its quasi-molecular scheme, is described. The code is used to simulate the shock compression of polycrystalline copper at 3.35 and 11.0 GPa. The model polycrystal has a normal distribution of grain sizes, with mean diameter 14 μm, and three distinct grain orientations are permitted with respect to the shock direction; 〈1 0 0〉, 〈1 1 0〉, and 〈1 1 1〉. Particle velocity dispersion (PVD) is present in the shock-induced flow, attaining its maximum magnitude at the plastic wave rise. PVD normalised to the average particle velocity of and are yielded for the 3.35 and 11.0 GPa shocks, respectively, and are of the same order as those seen in the experiment. Non-planar elastic and plastic wave fronts are present, the distribution in shock front position increasing with propagation distance. The rate of increase of the spread in shock front positions is found to be significantly smaller than that seen in probabilistic calculations on nickel polycrystals, and this difference is attributed, in the main, to grain interaction. Reflections at free surfaces yield a region of tension near to the target free surface. Due to the dispersive nature of the shock particle velocity and the non-planarity of the shock front, the tensile pressure is distributed. This may have implications for the spall strength, which are discussed. Simulations reveal a transient shear stress distribution behind the shock front. Such a distribution agrees with that put forward by Lipkin and Asay to explain the quasi-elastic reloading phenomenon. Simulation of reloading shocks show that the shear stress distribution can give rise to quasi-elastic reloading on the grain scale.     

Acoustoelastic effect and wave propagation in heterogeneous weakly anisotropic materials

A theoretical analysis of the acoustoelastic effect is presented. It is based upon the theory of sound wave propagation in a stressed heterogeneous weakly anisotropic elastic medium composed of grains. The effect of residual stress is included, and shown to be different from that of applied stress. The statistics of grain orientation and of grain correlation are taken into account. The acoustoelastic coefficients and the effects of dispersion, attenuation and symmetry of the medium are determined.     

A note on wave propagation in internally constrained hyperelastic materials

The purpose of this note is to recall and give simple proofs of general results relating to the speeds of propagation and polarization of waves propagating in internally constrained materials. Some of the results have been given previously but appear not to be as well known as they ought to be. Typical of the results is that for an incompressible hyperelastic body the squared wave speeds are real and the corresponding polarizations are orthogonal.     

Nonreciprocal and directional wave propagation in a two-dimensional lattice with bilinear properties

Nonlinear Dynamics - A passive method of realizing nonreciprocal wave propagation in a two-dimensional (2D) lattice is proposed, using bilinear springs combined with the necessary spatial asymmetry...     

Contrast of optical activity and rogue wave propagation in chiral materials

Nonlinear Dynamics - We report the contrast of optical activity and properties of nonparaxial optical rogue waves for the higher-order nonparaxial chiral nonlinear Schrödinger (NLS) equation....     

Buckling analysis of fibers in composite materials by wave propagation analogy

The analogy between the governing equations for the analysis of buckling in elastic structures and the elastodynamic equations of motion for wave propagation is presented. By employing this analogy, the exact and approximate buckling stresses of periodic layered materials and continuous fiber composites, respectively, are established. This is performed by utilizing micromechanically based dispersion relations for elastic wave propagating in the composite materials, which provide for a given wave length the corresponding phase velocity. By a specific change of variables in these dispersion relations, the corresponding buckling stresses can be determined. Results are presented and compared with solutions based on the mechanics of materials approach as well as with the well known Rosen’s fiber buckling predictions.     

Analysis of two-dimensional,finite amplitude wave propagation by time marching methods

Two-dimensional, finite-amplitude wave propagation in an inviscid, subsonic, perfect gas medium is analysed by explicit finite-difference methods. A two-step, Lax-Wendroff method and the single-step, Lax-Friedrichs method are used. A prescribed propagating velocity or pressure disturbance is applied along a single row of grid points normal to the stream direction and results in a 'forced' outflow boundary. The inflow boundary is placed far from outflow by utilizing a streamwise expanding grid and uniform inflow is imposed. Side boundaries are spatially periodic. The numerical solutions are compared with analytical small-perturbation solutions; higher-order effects arising from non-linearities are revealed by Fourier analysis. Solutions which closely approached a periodic state were obtained. The Lax-Wendroff method combined with the expanding grid is shown to be accurate and stable, the Lax-Friedrichs scheme produced highly damped solutions.     

Theoretical and numerical investigation of HF elastic wave propagation in two-dimensional periodic beam lattices

The elastic wave propagation phenomena in two-dimensional periodic beam lattices are studied by using the Bloch wave transform. The numerical modeling is applied to the hexagonal and the rectangular beam lattices, in which, both the in-plane （with respect to the lattice plane） and out-of-plane waves are considered. The dispersion relations are obtained by calculating the Bloch eigenfrequencies and eigenmodes. The frequency bandgaps are observed and the influence of the elastic and geometric properties of the primitive cell on the bandgaps is studied. By analyzing the phase and the group velocities of the Bloch wave modes, the anisotropic behaviors and the dispersive characteristics of the hexagonal beam lattice with respect to the wave prop- agation are highlighted in high frequency domains. One im- portant result presented herein is the comparison between the first Bloch wave modes to the membrane and bend- ing/transverse shear wave modes of the classical equivalent homogenized orthotropic plate model of the hexagonal beam lattice. It is shown that, in low frequency ranges, the homog- enized plate model can correctly represent both the in-plane and out-of-plane dynamic behaviors of the beam lattice, its frequency validity domain can be precisely evaluated thanks to the Bloch modal analysis. As another important and original result, we have highlighted the existence of the retro- propagating Bloch wave modes with a negative group veloc- ity, and of the corresponding ＂retro-propagating＂ frequency bands.