Peridynamic modeling of nonlinear surface acoustic waves propagating in orthotropic materials.

Due to the elastic nonlinearity of the material, high-amplitude surface acoustic waves undergo nonlinear evolution during propagation and may lead to material failure. To enable the acoustical quantification of material nonlinearity and strength, a comprehensive understanding of this nonlinear evolution is necessary. This paper presents a novel ordinary state-based nonlinear peridynamic model for the analysis of the nonlinear propagation of surface acoustic waves and brittle fracture in anisotropic elastic media. The relationship between seven peridynamic constants and second- and third-order elastic constants is established. The capability of the developed peridynamic model has been demonstrated by predicting surface strain profiles of surface acoustic waves after propagating in the silicon (111) plane and the 〈112¯ã€‰ direction. On this basis, the nonlinear wave-induced spatially localized dynamic fracture is also studied. The numerical results reproduce the main features of nonlinear surface acoustic waves and fracture observed in experiments.

Experimental testing and biomechanical CT analysis of Chinese cadaveric vertebrae with different modeling approaches.

Osteoporosis is characterized by reduced bone strength predisposing to an increased risk of fracture. Biomechanical computed tomography (BCT), predicting bone strength via CT-based finite element analysis (FEA), is now clinically available in the USA for diagnosing osteoporosis or assessing fracture risk. However, it has not been previously validated using a cohort of only Chinese subjects. Additionally, the effect of various modeling approaches on BCT outcomes remains elusive. To address these issues, we performed DXA and QCT scanning, compression testing, and BCT analyses on thirteen vertebrae derived from Chinese donors. Three BCT models were created (voxBCT and tetBCT: voxel-based and tetrahedral element-based FE models generated by a commercial software; matBCT: tetrahedral element-based FE model generated by a custom MATLAB program). BCT-computed outcomes were compared with experimental measures or between different BCT models. Results showed that, DXA-measured areal bone mineral density (aBMD) showed weak correlations with experimentally-measured vertebral stiffness (R2 = 0.28) and strength (R2 = 0.34). Compared to DXA-aBMD, BCT-computed stiffness provided improved correlations with experimentally-measured stiffness (voxBCT: R2 = 0.82; tetBCT: R2 = 0.77; matBCT: R2 = 0.76) and strength (voxBCT: R2 = 0.55; tetBCT: R2 = 0.57; matBCT: R2 = 0.53); BCT-computed mechanical parameters (stiffness, stress and strain) of the three different models were highly correlated with each other, with coefficient of determination (R2) values of 0.89-0.98. These results, based on a cohort of Chinese vertebral cadavers, suggest that BCT is superior over aBMD to consistently predict vertebral mechanical characteristics, regardless of the modeling approaches of choice.

Inversion of surface damage and residual stress in ground silicon wafers by laser surface acoustic wave technology.

The paper presents a study of surface acoustic waves propagation in a damage layer with finite thickness and residual stress on an orthotropic semi-infinite medium to reveal the application of laser ultrasound in the surface inspection of ground silicon wafers. Biot's theory of small deformations influenced by initial stress forms the basis for this study. Considering the case that the displacement and boundary forces are continuous at the interface and the forces vanish on the free surface, the required dispersion relation is obtained. We consider a sample of (100) silicon wafer by grinding with fine abrasive grains, which has a machined face with a micrometer-level thickness of surface damage and residual stress. In order to discuss the impact of propagation directions, degree of surface damage, residual compressive stress on the velocity characteristics of surface waves, the numerical computation of the dispersion equations is performed. It has been found that surface damage has a significant effect on the dispersion curve, while the residual compressive stress can only cause a small decrease Δc in the surface wave velocity. The velocity decrease Δc becomes obvious at high frequencies. For a fixed residual compressive stress and frequency, Δc hardly changes with the degree of surface damage and propagation directions. Based on the above characteristics, we study the inverse problem on detecting both surface damage and residual stress simultaneously by SAW velocities and give a corresponding iterative algorithm. This study may provide theoretical guidance for non-destructive testing of residual stress.

Time-frequency analysis of laser-excited surface acoustic waves based on synchrosqueezing transform.

Laser-excited surface acoustic wave (LSAW) techniques can realize the measurement of surface properties through dispersion curve inversion. In addition to the conventional phase spectrum method, time-frequency analysis can also be used as a calculation tool for the dispersion curve. An accurate time-frequency analysis method is important in precisely inverting the surface properties. In this paper, synchrosqueezing transform (SST) is applied to the analysis of LSAW. By comparing the processing results of the constructed LSAW signal, SST shows higher time-frequency resolution and robustness than other common time-frequency analysis algorithms. Finite element model is used to simulate the propagation of LSAW in the film/substrate structure. And SST is used to calculate the dispersion curve of SAW information extracted during the simulation. A fast algorithm is introduced, where the film thickness is initially estimated by calculating the midrange. Through inversion, the resulting film thickness error is only 1.20% from the theoretical value. Therefore, SST is an effective tool for analyzing LSAW and calculating its dispersion curve.

Analysis of velocity calculation methods of laser-induced surface acoustic wave.

The key to measuring residual stress by surface acoustic wave method is the accurate measurement of velocity. In this paper, the velocity of laser-induced broadband surface acoustic wave is studied, and three velocity calculation methods of surface acoustic wave, time domain method, phase method and wavelet method are compared. The calculation error of the time domain method under the condition of dispersion is analyzed. A recursive method for calculating phase difference is proposed to improve the efficiency of phase method. The simulated surface acoustic waves are used to compare the phase method and wavelet method under the conditions of attenuation and dispersion. Compared with the wavelet method, the phase method cannot distinguish the time when the frequency band appears, and the velocity calculation of adjacent frequency points is related, while the wavelet method is independent of each other. The wavelet method can improve the calculation accuracy of the velocity curve by interpolating the original data. After interpolation, the trend of curve is more obvious, and the fitting error is greatly reduced.