The last few decades have seen great achievements in dynamic fracture mechanics. Yet it was not possible to experimentally quantify the full-field behavior of dynamic fractures, until very recently. Here we review our recent work on the full-field quantification of the temporal evolution of dynamic shear ruptures. Our newly developed approach based on digital image correlation combined with ultrahigh-speed photography has revolutionized the capabilities of measuring highly transient phenomena and enabled addressing key questions of rupture dynamics, including the visualization of the complete displacement, particle velocity, strain, stress and strain rate fields near growing ruptures, the evolution of dynamic friction during individual rupture growth, and the detailed study of rupture speed limits. For example, dynamic friction has been the biggest unknown controlling how frictional ruptures develop but it has been impossible, until now, to measure dynamic friction during spontaneous rupture propagation and to understand its dependence on other quantities. Our recent measurements allow, by simultaneously tracking tractions and sliding speeds on the rupturing interface, to disentangle its complex dependence on slip, slip velocity, and on their history. In another application, we have uncovered new phenomena that could not be detected with previous methods, such as the formation of pressure shock fronts associated with “supersonic” propagation of shear ruptures in viscoelastic materials where the wave speeds are shown to depend strongly on the strain rate field and to also vary substantially across the field.

Phononic crystals composed of delicately designed periodic units are used to control spatial and spectral properties of acoustic or elastic waves. The ability to manipulate transmitting waves in a real-time dynamic manner provides a new concept in programable phononic crystals and metamaterials. In this study, the mechanical waves and bandgaps in a two-dimensional spring-mass array loaded by high-frequency parametric excitation have been investigated by both analytical and numerical methods. It is found that the high-frequency parametric excitation provides an equivalent additional stiffness which leads to low-frequency bandgaps. By tuning the parametric excitation, the versatility of such a dynamic modulating technique has been presented. The waveguide structure has also been designed and studied by non-uniformly distributed parametric excitations.

Nonlinear interaction of Lamb waves with an imperfect joint of plates for the incidence of the lowest-order symmetric (S0) Lamb wave is investigated by perturbation analysis and time-domain numerical simulation. The imperfect joint is modeled as a nonlinear spring-type interface, which expresses interfacial stresses as functions of the displacement discontinuities. In the perturbation analysis, under the assumption of weak nonlinearity, the second-harmonic generation at the joint is examined in the frequency domain by the thin-plate approximation using extensional waves. As a result, the amplitude of the second-harmonic extensional wave is shown to be in good agreement with the result of the S0 mode in a low-frequency range. However, it is found that the thin-plate approximation does not reproduce the amplification of the second-harmonic S0 mode, which occurs due to the resonance of the joint. Furthermore, the time-domain analysis is performed by the elastodynamic finite integration technique (EFIT). When the amplitude of the incident wave is relatively large, the fundamental wave and the second harmonic exhibit different behavior from the results by the perturbation analysis. Specifically, if the incident amplitude is increased, the peak frequency of the second-harmonic amplitude becomes low. The transient behavior of the nonlinear interaction is also examined and discussed based on the results for the weak nonlinearity.

We investigate the behavior of soft magnetoactive periodic laminates under remotely applied magnetic field. We derive explicit formulae for the induced deformation due to magnetic excitation of the laminates with hyperelastic magnetoactive phases. Next, we obtain the closed-form formulae for the velocities of long transverse waves. We show the dependence of the wave velocity on the applied magnetic intensity and induced strains, as well as on the wave propagation direction. Based on the long wave analysis, we derive closed-form formulae for the critical magnetic field corresponding to the loss of macroscopic stability. Finally, we analyze the transverse wave band gaps appearing in magnetoactive laminates in the direction normal to the layers. We illustrate the band gap tunability—width and position—by magnetically induced deformation.

Most soft materials resist volumetric changes much more than shape distortions. This experimental observation led to the introduction of the incompressibility constraint in the constitutive description of soft materials. The incompressibility constraint provides analytical solutions for problems which, otherwise, could be solved numerically only. However, in the present work, we show that the enforcement of the incompressibility constraint in the analysis of the failure of soft materials can lead to somewhat nonphysical results. We use hyperelasticity with energy limiters to describe the material failure, which starts via the violation of the condition of strong ellipticity. This mathematical condition physically means inability of the material to propagate superimposed waves because cracks nucleate perpendicular to the direction of a possible wave propagation. By enforcing the incompressibility constraint, we sort out longitudinal waves, and consequently, we can miss cracks perpendicular to longitudinal waves. In the present work, we show that such scenario, indeed, occurs in the problems of uniaxial tension and pure shear of natural rubber. We also find that the suppression of longitudinal waves via the incompressibility constraint does not affect the consideration of the material failure in equibiaxial tension and the practically relevant problem of the failure of rubber bearings under combined shear and compression.

Protecting concrete structures from high energetic dynamic events such as blasts and impact is a major concern, in both civil- and military-related applications. Most conventional techniques fail to counter the unpredictable nature of dynamic loads, as well as the complex response of structures due to stress wave propagation. Hence, this paper explores the possibility of using a functionally graded—according to impedance—metallic composite system as a protective mechanism to a concrete structure. An analytical framework was developed using matlab , based on elastic and shock wave propagation theories, especially incorporating multiple interactions within the composite system, as well as reflections of free surfaces. A numerical analysis was carried out using the advanced finite element code LS-DYNA. The main objective of this paper was to compare the performance of the composite system against the conventional monolithic system.

Wrinkling is a common phenomenon in natural and engineering film structures. The wrinkles influence the geometry and dynamic response of these structures. In this work, we investigate the wrinkling of a stretched thin film containing engineered microstructures and its derived functionality on controlling the propagation of bending waves. The underlying mechanism is revealed and the effect of wrinkles on the bandgap of bending waves is systematically evaluated via numerical simulations based on the Bloch wave theory. We show that wrinkles with a customized wavelength can be triggered in the microstructured film due to the mismatched deformation in the film. The bandgap of the wrinkled film can be finely tuned via applied stretching, resulting in the controllable propagation of bending waves in thin films. Our work provides fundamental insights into wave propagation in wrinkled films and potential applications for dynamic control of the wave propagation in engineering film structures.

This paper presents an innovative approach of stress attenuation through a continuous impedance-graded material system for high strain-rate events. High energetic dynamic events such as blasts and impact could cause stress waves—in the form of elastic, plastic, and shock—to propagate in a solid material. An impedance-graded composite is created by arranging different metallic alloys in the reducing order of their impedance through the system. Impedance, which is the product of volumetric mass density and wave velocity, is chosen as the function as it plays a governing role in elastic, plastic, and shock waves. An analytical framework to quantify the stress wave propagation through an impedance-graded multimaterial system is developed based on the principles of shock and elastic wave theories. The numerical simulations carried out using nonlinear finite element code, LS-DYNA, were able to capture and quantify the elastic, plastic, and shock waves and their reflections at different interfaces. It was identified that the final transmitted stress wave, which could comprise elastic, plastic, and shock waves, as well as the reflected tensile elastic wave at each material interface, needs to be controlled in order to develop a robust multimaterial system.

This work examines elastic wave propagation phenomena in open-cell foams with the use of the Bloch wave method and finite element analysis. Random foam topologies are generated with the Surface Evolver and subsequently meshed with Timoshenko beam elements, creating open-cell foam models. Convergence studies on band diagrams of different domain sizes indicate that a representative volume element (RVE) consists of at least 8 3 cells. Wave directionality and energy flow features are investigated by extracting phase and group velocity plots. Explicit dynamic simulations are performed on finite size domains of the considered foam structure to validate the RVE results. The effect of topological disorder is studied in detail, and excellent agreement is found between the wave behavior of the random foam and that of both the regular and perturbed Kelvin foams in the low-frequency regime. In higher modes and frequencies, however, as the wavelengths become smaller, disorder has a significant effect and the deviation between regular and random foam increases significantly.

Predeformation simultaneously changes the effective material stiffness as well as the geometric configuration and therefore may be utilized to tune wave propagation in soft phononic crystals (PCs). Moreover, the band gaps of soft PCs, as compared with those of the hard ones, are more sensitive to the external mechanical stimuli. A one-dimensional tunable soft acoustic diode based on soft functionally graded (FG) PCs is proposed. The two-way asymmetric propagation behavior is studied at the resonant frequency within the band gap. Numerical results show that the operating frequency (i.e., the resonant peak) of the soft graded acoustic diode can be altered by adjusting the mechanical biasing fields (including the longitudinal prestress and the lateral equibiaxial tension). The adjustment becomes significant when the strain-stiffening effect of the Gent hyperelastic material is properly harnessed. Furthermore, the prestress or equibiaxial tension can affect the two-way filtering of the soft FG PC in a separate and different manner. In addition, it is much easier to realize the tunable acoustic diode by exploiting soft FG materials with stronger compressibility. It is shown that the introduction of acoustic impedance is beneficial for predicting the tunable effects. The simulations and conclusions should provide a solid guidance for the design of tunable two-way unidirectional acoustic diodes made from soft hyperelastic materials.

We experimentally study the dynamic behavior of a belt-drive system to explore the effect of loading conditions, driving speed, and system inertia on both the frequency and amplitude of the observed frictional and rotational instabilities. A self-excited oscillation is reported whereby local detachment events in the belt–pulley interface serve as harmonic forcing of the pulley, leading to angular velocity oscillations that grow in time. Both the frictional instabilities and the pulley oscillations depend strongly on operating conditions and system inertia, and differ between the driver and driven pulleys. A larger net torque applied to the pulley generally intensifies Schallamach waves of detachment in the driver case but has little influence on other measured response quantities. Higher driving speeds accelerate the occurrence of frictional instabilities as well as pulley oscillations in both cases. Increasing the system's inertia does not affect the behavior of contact instabilities, but does lead to a steadier rotation of the pulley and more pronounced fluctuations in the belt tension. A simple dynamic model of the belt-drive system demonstrates good agreement with the experimental results and provides strong evidence that frictional instabilities are the primary source of the system's self-oscillation.

A new type of all-solid metamaterial model with anisotropic density and fluid-like elasticity is proposed for controlling acoustic propagation in an underwater environment. The model consists of a regular hexagonal lattice as the host that defines the overall isotropic stiffness, in which all lattice beams have been sharpened at both ends to significantly diminish the shear resistance. The inclusion structure, which involves epoxy, rubber, and lead material constituents, is designed to attain a large density–anisotropy ratio in the broad frequency range. The wave-control capability of metamaterials is evaluated in terms of underwater acoustic stretching, shifting, and ground cloaking, which are generated by the transformation acoustic method. The decoupling design method was developed for the metamaterial microstructure using band-structure, effective-medium, and modal-field analyses. The acoustic performance of these metamaterial devices was finally verified with full-wave numerical simulations. Our study provides new insight into broadband underwater acoustic manipulation by all-solid anisotropic-density metamaterials.

This study investigates the significance of fluid–structure interaction (FSI) effects on structural response to pressure wave and shock wave loading. Finite element (FE) simulations and one-dimensional (1D) analytical models are used to compare the responses of simple structures in presence and absence of FSI. Results are provided in nondimensional form and allow rapid estimation of the significance of FSI. The cases of a square elastic plate in bending and a square rigid-perfectly plastic plate undergoing membrane stretching are discussed in detail. We deduce simple formulae to identify scenarios in which effects of FSI can be neglected.

The transverse ballistic impact on a two-dimensional (2D) membrane causes a truncated deformation cone to develop in the wake of tensile implosion waves. Here, the cone wave reflected from the finite boundaries of the elastic membrane has been studied analytically. A first-order linear nonhomogeneous differential equation for the ratio of the reflected cone wave front velocity to the speed of tensile waves is derived, which is further used to calculate the traveling time taken by the reflected cone wave to reach to the projectile surface. Since the reflected wave starts when the membrane is already in a deformed configuration, the speed of the reflected cone wave is a function of radius r in the cylindrical coordinates as opposed to almost constant speed of the incoming cone wave studied in the literature. The analytical results are validated with molecular dynamics (MD) simulations of the ballistic impact of projectiles onto a single layer of coarse-grained (CG) graphene. In the second part of the paper, we analyze the membrane impact problem for linear isotropic viscoelastic materials and find that the tensile wave speed for stresses and displacements is the same as that obtained in the case of a linear isotropic elastic material. We also show that only under special conditions, self-similar solutions for the cone wave are possible in viscoelastic materials modeled by Maxwell, Kelvin–Voigt, or a combination of similar models. Our findings lay some grounds on which further studies on the ballistic response of viscoelastic materials can be performed.

This work presents a theoretical method for surface love waves in poroelastic media loaded with a viscous fluid. A complex analytic form of the dispersion equation of surface love waves has been developed using an original resolution based on pressure–displacement formulation. The obtained complex dispersion equation was separated in real and imaginary parts. mathematica software was used to solve the resulting nonlinear system of equations. The effects of surface layer porosity and fluid viscosity on the phase velocity and the wave attenuation dispersion curves are inspected. The numerical solutions show that the wave attenuation and phase velocity variation strongly depend on the fluid viscosity, surface layer porosity, and wave frequency. To validate the original theoretical resolution, the results in literature in the case of an homogeneous isotropic surface layer are used. The results of various investigations on love wave propagation can serve as benchmark solutions in design of fluid viscosity sensors, in nondestructive testing (NDT) and geophysics.

This paper studies a new comprehensive model for toppling dynamics of regularly spaced dominoes in an array. The model has unlocked the hypotheses introduced by Stronge and Shu (Stronge, W. J., and Shu, D., 1988, “The Domino Effect: Successive Destabilization by Cooperative Neighbours,” Proc. R. Soc. A, 418 (1854), pp. 155–163), which can provide us some essential insights into the mechanism of domino wave. Extensive comparisons are made between the proposed model and the experimental results studied in the existing literature. Our numerical studies show that the existing theoretical models are special cases of the proposed model, and the fluctuation in the waveform of propagation speed observed from experiments was caused by the irregular multiple impacts between colliding dominoes. The influence of physical parameters of domino on the natural speed of toppling dominoes is also considered, and it is found that the coefficients of friction and restitution between colliding dominoes have more effects due to the energy dissipation during impact.

The idealized inverse-opal lattice is a network of slender struts that has cubic symmetry. We analytically investigate the elastoplastic properties of the idealized inverse-opal lattice. The analysis reveals that the inverse-opal lattice is bending-dominated under all loadings, except under pure hydrostatic compression or tension. Under hydrostatic loading, the lattice exhibits a stretching dominated behavior. Interestingly, for this lattice, Young's modulus and shear modulus are equal in magnitude. The analytical estimates for the elastic constants and yield behavior are validated by performing unit-cell finite element (FE) simulations. The hydrostatic buckling response of the idealized inverse-opal lattice is also investigated using the Floquet–Bloch wave method.

In order to design phononic crystals whose band-gaps are located in low-frequency ranges, researchers commonly adopt low stiffness polymeric materials as key constituents and exploit the high impedance mismatch between metals and polymers. However, there has been very little research on wave propagation at arbitrary angles in the sagittal plane of viscoelastic-elastic multilayered composites because there exist the intricate wave attenuation characteristics at the layer interfaces. The objective of our investigation is to obtain analytical dispersion relation for oblique wave motion in the sagittal plane of infinitely periodic multilayered composite composed of alternating viscoelastic and elastic solids, where the attenuation of harmonic plane waves is found to occur only in the direction perpendicular to the layers. By using this wave propagation characteristic, we directly apply the semi-analytical approach employed in elastic multilayered composites to calculate the dispersion relation of sagittal plane waves in alternating viscoelastic-elastic multilayered composites. Specifically, we consider a bilayered composite composed of alternating aluminum and polyurethane elastomer, whose complex-valued viscoelastic moduli are experimentally determined by performing dynamic mechanical analysis (DMA). The analysis shows that the alternating viscoelastic-elastic layered composite does not possess a phononic band-gap regardless of incident angles. In addition, wave motions at oblique angles are found to travel with a wide range of frequency contents compared to wave motions perpendicular to the layers. The presented analysis demonstrates that wave dispersion relation in viscoelastic-elastic layered composites is distinctly different from the corresponding elastic counterpart, and highlights the importance of the viscoelastic modeling of polymeric materials in wave dispersion analysis.

This paper discusses the dynamic interaction between a monoatomic chain of solid particles and a thin-walled spherical pressure vessel. The objective is to find a relationship between the highly nonlinear solitary waves (HNSWs) propagating within the chain and the internal pressure of the vessel. The paper introduces first a general finite element model to predict the abovementioned interaction, and then a specific application to tennis balls. The scope is to demonstrate a new nondestructive testing (NDT) method to infer the internal pressure of the balls. The overarching idea is that a mechanically induced solitary pulse propagating within the chain interacts with the thin-walled ball to be probed. At the chain–ball interface, the acoustic pulse is partially reflected back to the chain and partially deforms the rubber giving rise to secondary pulses. The research hypothesis is that one or more features of the reflected waves are monotonically dependent on the internal pressure. Both numerical and experimental results demonstrate a monotonic relationship between the time of flight (TOF) of the solitary waves and the internal pressure of the tennis balls. In addition, the pressure inferred nondestructively with the HNSWs matches very well the pressure measured destructively with an ad hoc pressure gauge needle. In the future, the results presented in this study could be used to develop a portable device to infer anytime anywhere the internal pressure of deformable systems (including biological systems) for which conventional pressure gages cannot be used noninvasively.

This investigation considers the dynamic stability of the steady-state frictional sliding of a finite-thickness elastic layer pressed against a moving rigid and flat surface of infinite extent. The elastic layer is fixed on its bottom surface; on its entire top surface, the rigid surface slides with constant speed and with a constant friction coefficient. The plane-strain equations of motion for a linear isotropic elastic solid are solved analytically for small dynamic disturbances. The analysis shows that even with a constant (speed-independent) friction coefficient, the steady solution is dynamically unstable for any finite friction coefficient. Eigenvalues with positive real parts lead to self-excited vibrations which occur for any sliding speed and which increase with increasing coefficient of friction. This is in contrast to the behavior of an elastic half-space sliding against a rigid surface in which the instability only occurs if the coefficient of friction is greater than unity. This work and its extensions are expected to be relevant in the theoretical aspects of sliding friction as well as in a variety of areas such as earthquake motion and brake dynamics.