Stress wave transmission and reflection through auxetic solids

Stress wave micro–macro attenuation in ceramic plates made of tiles during ballistic impact

This chapter explores the stress wave transmission and reflection from an incident stress wave , between isotropic solids of different Poisson’s ratio, with special emphasis on systems in which at least one of the solids is auxetic. The dimensionless transmitted stress, in terms of the ratio of transmitted to incident stresses, were investigated for longitudinal stresses in prismatic bars (1D stress), longitudinal stresses in width-constrained plates (2D stress or 2D strain), plane waves of dilatation (1D strain), torsional waves (shear waves), and Rayleigh (surface) waves. Each of these wave transmission study was performed under three special cases, i.e. when the (i) product of density and Young’s modulus for both solids are equal, (ii) product of density and shear modulus for both solids are equal, and (iii) product of density and bulk modulus for both solids are equal. Under these special conditions, results show that the stress transmission is effectively doubled or eliminated when the Poisson’s ratio for the isotropic solids are at their limits.

In an infinite elastic medium dilatational waves exhibit much more nonlinear distortion than do shear waves, but such behavior cannot be assumed when a boundary, such as a free surface, is present. Because of the process of mode conversion, a dilatational (P) wave that has already undergone significant distortion prior to its incidence at the boundary must impart its distortion to both the reflected P and vertically polarized shear (SV) wave. The problem of oblique incidence at a free surface was previously considered by us [1,2]. The present paper generalizes that analysis by permitting the boundary conditions at the planar interface to be arbitrary, and also by considering critical and supercritical angles of incidence.

To investigate the influence of nonparallel end‐surface on stress uniformity during loading process in rock SHPB test, SHPB numerical simulations have been carried out by LS‐DYNA when end‐face nonparallelism is within 0.40% and Young’s modulus ranges from 14 GPa to 42 GPa. Isotropic linear elastic model is applied for elastic steel pressure bar, and HJC constitutive model is chosen for rock specimen. Numerical simulation results indicate that fluctuation effect exists in both reflected stress waves and transmitted stress waves, and it is enhanced with the increase of end‐surface nonparallelism. The stress nonuniformity coefficient attenuates in a serrated fluctuation. With the increase of end‐surface nonparallelism, the amplitude of transmitted stress wave gradually reduces, while stress nonuniformity coefficient increases. Stress equilibrium time first decreases slightly then increases in a step type. Therefore, nonparallel end‐surface leads to two reverse results for stress uniformity during SHPB loading process, extending stress equilibrium time and shortening stress equilibrium time. And the influence on shortening stress equilibrium time is weak, while the influence on extending stress equilibrium time is great. When end‐surface nonparallelism is 0.10%, stress equilibrium time achieves its lowest value whatever Young’s modulus is. Hence, end‐surface nonparallelism of the rock specimen is suggested to be controlled within 0.10% when conducting SHPB tests.

During the process of rock dynamic fracture, the rock mass releases a huge amount of fracture energy, which primarily transforms into a strong stress wave; the stress wave can cause serious damage to the neighboring zones when passing through the structural rock medium. In this study, the transmission and frequency features of the stress wave through cemented joints are investigated. The polyurethane (PU) is chosen as the cementing material to glue the cut faces of the rock sample. The bonding stiffness of joints is adjusted by the mixing proportion of the polyurethane diluent. By conducting the Split Hopkinson Pressure Bar (SHPB) test, the effect of the stiffness and thickness of the PU adhesive layer is studied by monitoring the coefficients of reflection, transmission, and dissipation, as well as the frequency components. The testing results indicate that the transmission effect increases significantly, whereas the dissipation decreases with the growth of the bonding stiffness. The increasing impact energy results in a higher degree of body fracture and crack density. The low-pass filtering (LPF) effect of the stress wave is observed evidently in low bonding stiffness.

when explosive blasts in the rock, the stress wave of impact produced appears all kinds of phenomena, such as reflection, refraction, and transmission in the process of transmission on the joint surface because of discontinuity, heterogeneity and anisotropy of rock mass of weak plane in physics, which lead to extremely complex on rock blasting process. Through conducting on high dynamic strain test of blasting process on joint rock mass model, it researches dynamic load characteristics of joint rock mass and joint-planes effect on extension of critical raw crack and attenuation law of stress wave, analyzes the strain waveform of strain gages which locate in the different direction between initial crack of blasting and joint, and figures out the impact of joint plane on the stress wave transmission, which provide an important theoretical basis on the relevant parameters design in the process of blasting engineering of joint mass existing in actual.

In order to study the dynamic mechanical properties and stress wave propagation law of coal rock bodies with different joint matching coefficients under combined dynamic and static loads, dynamic impact tests were conducted for artificial jointed coal samples by using coupled static and dynamic loads based on SHPB device. The test result indicated that as the joint matching coefficient JMC decreases, the transmittance wave amplitude drops. While the transmittance coefficient T decreases as the joint matching coefficient JMC lowers, the static load steadily increases to boost the contact effect between artificially jointed coal samples, hence increasing the transmittance coefficient T. And the specimen’s stress wave transmission enhancement and energy dissipation declined when the joint matching coefficient JMC and static load increased. As a consequence, in underground engineering, greater attention should be paid to the combined effect of joint and static load on the influence of stress wave transmission characteristics.

The combined finite–discrete element method (FDEM) is an advanced numerical calculation method that is highly suitable for simulating the entire rock blasting process. Considering that rock mass contains many joints, the present study introduces a rock joint constitutive model to capture the transmission and reflection phenomena of blasting stress waves when they reach the joint. At the same time, based on the original FDEM code, an optimized blasting calculation model is proposed. This model considers the effect of explosive gas and accurately describes the physical relationship between the explosive gas pressure and the change in the blasting chamber area caused by crack propagation. To overcome the limitation of previous blasting models that only apply the pressure of the explosive gas to the borehole wall, the present study optimizes the determination conditions for crack penetration and the calculation method for the blasting chamber area as well as further considered the influence of the embedding effect of explosive gas on crack propagation. Finally, through three examples, the transmission and reflection laws of stress waves at the joints and the entire process of rock mass throw blasting are simulated. The results illustrate that this model can capture the propagation of stress waves, the gas wedge effect of explosive gas, and the entire process of crack initiation, propagation, and penetration in the rock mass during the explosion, demonstrating the potential of FDEM in blasting simulation.

TRANSIENT AXISYMMETRIC STRESS WAVE PROPAGATION IN WEAKLY COUPLED LAYERED STRUCTURES

The stress wave reflection method is widely used in the detection of structure size and integrity due to its advantages of low environmental impact and convenience. The detection accuracy depends on the accurate extraction of the stress wave reflection period. The traditional peak–peak method (PPM) measures the time interval between the first two peaks of the reflected waves to extract the reflection period. However, human interpretation is not avoidable for identifying the weak peak due to signal energy leaks into the surrounding environment. This paper proposes an algorithm for automatic extraction of the stress wave reflection period based on image processing to avoid human interference. The image is the short-time Fourier transform (STFT) spectrogram of the reflected wave signal after applying wavelet denoising and quadratic self-correlation operations. The edge detection method of image processing is used to extract the periodically occurring trough in the image. Graying and filtering are performed to eliminate interference. The frequency of the trough distribution is calculated by using the fast Fourier transform (FFT), and then the reflection period of the stress wave is obtained. The effectiveness and accuracy of the proposed method are validated by measuring the different lengths of two buried metal piles in soil. Comparing with the existing method of extracting the stress wave reflection period, this new algorithm comprehensively utilizes the time–frequency domain information of the stress wave reflection signal.

Upon stress wave interaction with joints, incident energy is reflected and refracted. To gain insight into the mechanisms associated with dynamic processes such as blasting, percussion drilling and seismicity, knowledge of the amplitudes of the reflected and refracted waves is of importance. This paper compiles stress, energy, displacement and velocity amplitudes of stress waves, which are reflected and refracted by a variety of interface types. In addition to covering the well-known wave interactions with standard discontinuities, such as a free boundary and welded interface, some new interface conditions are analysed, e.g. interfaces with friction and shear strength, and interfaces with normal and shear stiffness related to measurable rock properties. The aim of this tutorial paper is to act as an educational guide and reference for the blasting engineer, seismologist, geophysicist and rock engineer, and to assist in further understanding stress wave interactions with rock mass discontinuities.

When stress waves interact with joints and fractures in a rock mass, the incident energy is reflected from and refracted (transmitted) across the interface. Knowledge of the amplitudes of reflected and transmitted waves is of importance to understand stress wave propagation through discontinuous rock, and to assess the stability and ultimately the safety of structures in rock loaded transiently. In this paper the dynamic behaviour of joints containing fluids or thin layers of comparatively soft material are analysed. A generalised Kelvin model is used to simulate the interactions of incident P- and SV-waves. It is found that the amplitudes of the reflected and refracted waves are dependent on the joint stiffness and viscosity, as well as the frequency of the incident wave. The energy dissipation of the viscous interface is analysed and parameters influencing the maximum dissipation are quantified and discussed.

The passage of stress waves of large amplitude through solid specimens often produces fractures which differ in several respects from those which can occur under any other conditions. Many of the observed phenomena can be accounted for in terms of the acoustical treatment of reflection and refraction of stress waves at the boundaries of the specimen and of diffraction effects in regions where the dimensions of the specimen become comparable with the wavelength of the disturbance. When a fracture occurs it results in a sudden release of stress, and consequently, secondary stress waves travel out from the fracture surfaces. The experimental investigation of these effects by means of high-speed photography, by electrical measurements of stress and strain, and by subsequent examination of the geometry and appearance of the fractured surfaces will be described, and the type of information which such investigations may give about the nature of the phenomenon of brittle fracture will be discussed.

Transmission and reflection of acoustic waves from a layer of a bubble medium into a liquid is theoretically studied, with subsequent reflection of the waves that arise from the rigid wall. The amplitudes of the emerging waves are determined through the amplitude of the initial wave, analytical expressions are obtained for the coefficients of reflection and transmission of waves across the interfaces.

Reflected and transmitted waves in a channel with side porous mattresses