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Previous experimental and computational results have confirmed that the thermal conductivity of a two-dimensional (2D) material can be considerably affected by strain. Numerous attention has been paid to explore the relevant mechanisms. However, the strain effects on the interfacial thermal conductance (ITC) of 2D heterostructure have attracted little attention. Herein, the non-equilibrium molecular dynamics (NEMD) simulations were conducted to the graphene/hexagonal boron nitride (GR/h-BN) heterostructure to investigate the strain effects on the ITC. Three types of strains were considered, i.e., tensile strain, compressive strain, and shear strain. The results indicate that the strain can adjust the ITC for the GR/h-BN heterostructure effectively, and the strain loading direction also influences the ITC. Generally, the tensile strain reduces the ITC of the heterostructure, in addition to the BN-C system at small tensile strain; both the compressive strain and shear strain increase the ITC, especially at a small strain. For the NB-C system, it is more sensitive to the strain loading direction and the yx shear strain of 0.06 is the most effective way to strengthen the ITC. Our results also show that the out-of-plane deformation weakens the in-plane vibration of atoms, leading to a reduction of the interfacial thermal energy transport.

In recent years, PVDF(polyvinylidene fluoride) and its copolymers have attracted great attention in the development of energy-harvesting devices because of their unique properties such as good flexibility, environmental friendliness, high halogen and acid resistance, lightweight and good biocompatibility. Compared to the most commonly used PZT (lead zirconate titanate), the piezoelectricity of PVDF and its copolymer-based materials is relatively low. To further expand the applications of PVDF, there is an urgent need for efficient methods to prepare high piezoelectric polymers or composites. In this work, the crystal phases are introduced first. Then, the preparation methods of PVDF and its copolymer-based materials are summarized, which are mainly focused on four determining factors of piezoelectricity. The mechanisms of piezoelectric β-phase formation and α- to β-phase transformation are introduced. The influence parameters of each process and their interactions are discussed in detail. In the last section, the progress of the preparation methods is summarized. This work will provide useful information to researchers working on piezoelectric composites.

In this work, we propose an asymmetric transmission structure (ATS) for elastic shear vertical (SV) waves in solids, which has been relatively unexplored. The ATS is constituted by a metasurface and a phononic crystal (PC) possessing a directional band gap. While the metasurface aims to redirect the incident wave, the PC acts as a directional filter. The metasurface is composed of a stacked array of composite plates with two connecting parts made of different materials. To examine the performance of the designed ATS, full numerical simulations have been conducted. The numerical results indicate that the proposed ATS offered a relatively broad working frequency band and had a one order of magnitude difference in terms of transmission between the positive and negative incidences. Our study provides an alternative method to control elastic SV waves and could benefit applications in various fields, such as Micro-Electro-Mechanical System (MEMS), in which thin plates are frequently used components.

We report a novel approach to control flexural waves in thin plates using metasurfaces constituted of an array of parallel arranged composite beams with their neutral planes the same as that of the host plate. The composite beams are composed of two connecting parts made of different materials, and have a thickness identical to that of the host plate. To steer flexural waves in thin plates, a rectangular zone is subtracted from the thin plate and is then filled with the designed metasurface. The time delay of flexural waves in each composite beam of the metasurface is tuned through the varying length of the two connecting components, while keeping the total length fixed. To quantitatively evaluate the time delay in each composite beam, a theoretical model for analyzing the phase of the transmitted flexural waves is developed based on both Mindlin plate theory and Timoshenko beam theory. To control the flexural waves at will, each composite beam in the metasurface is delicately designed according to the proposed theoretical model. For illustrative purposes, the refracted and focusing metasurfaces are designed and numerically validated.

Poly(vinylidene difluoride)(PVDF) and its copolymers are promising materials to fabricate self-powered devices, while their relatively low power generation capability limits their applications. In this work, graphene was added into poly(vinylidene-trifluoroethylene)(PVDF-TrFE) to prepare excellent piezoelectric composite films by a solution-casting method. The PVDF-TrFE/graphene containing 0.15 wt% graphene generated a calibrated open circuit of 12.43 V, which is 104% higher than that without graphene. Similarly, the harvested power density was increased by 302% (AC circuit) and 359% (DC circuit), respectively. The XRD spectra indicate that the PVDF-TrFE/graphene with an extremely low content of graphene did not work well on the phase formation in the initial crystallization. The crystallinity degree of the untreated films was about 40%. After stretching, the crystallinity degree increased to above 60%, especially for the films containing 0.15 wt% graphene (67%). Hence, stretching was the main factor to increase the crystallinity degree. This study also confirmed that the heat treatment could further improve the crystallinity of the stretched films to some extent.

In this study, carbon black (CB)/multi-walled carbon nanotube (MWCNT)/polyvinylidene fluoride-hexafluoropropylene (PVDF-HFP) composite films were fabricated as strain sensors. The sensing characteristics of the composite films both in the direct current (DC) and alternating current (AC) circuits were systematically tested. It was found that the hybrid nanofiller could effectively improve both the electrical conductivity and the sensitivity of the nanocomposites at a given loading far below the percolation threshold of a single filler. At 3.0% tensile strain, the highest DC and AC gauge factors for the nanocomposites with 1.0 wt.% CB and 0.1 wt.% MWCNT were 10.67 and 10.38, respectively, which were 1992.2% and 75.9% higher than those of the composites filled with 2.0 wt.% CB only. In addition, both the relationship of the strain-resistance change rate in the DC condition and the strain-DLT (the dielectric loss tangent) change rate in the AC condition of the nanocomposites with the hybrid nanofiller showed an approximatively linear characteristic, which demonstrated that the linearity of the nanocomposite sensor could be controlled by properly adjusting the content of CB and MWCNT. Finally, the mechanism of the synergistic effect was investigated by inspecting the microstructure of the nanocomposites and an equivalent RLC circuit model.

Ti matrix composites reinforced with 1–5 wt% graphene oxide (GO) were prepared by hot-pressed sintering in argon atmosphere. The effect of sintering temperature on the microstructures and mechanical properties of the composite was also evaluated. The results show that TiC nanoparticles were formed in situ as interfacial products via the reaction between Ti and GO during sintering. With increases in GO content and sintering temperature, the amount of TiC increased, improving the mechanical properties of the composites. GO was also partly retained with a lamellar structure after sintering. The composite reinforced with 5 wt% GO exhibited a hardness of 457 HV, 48.4% higher than that of pure Ti at 1473 K. The Ti-2.5 wt% GO composite sintered at 1473 K achieved a maximum yield stress of 1294 MPa, which was 62.7 % higher than that of pure Ti. Further increasing the GO content to 5 wt% led to a slight decrease in yield stress owing to GO agglomeration. The fracture morphology of the composite reinforced with GO exhibited a quasi-cleavage fracture, whereas that of the pure Ti matrix showed a ductile fracture. The main strengthening mechanism included grain refinement, solution strengthening, and dispersion strengthening of TiC and GO.

Because of the difficulty in quantifying weak nonlinear Lamb waves in strong noises, the second harmonic generated by material nonlinearity or microcontact crack is detected using the Duffing-Van der Pol oscillator (DVPO), and its relative intensity is quantified based on the periodic trajectory area exponent (PTAE) of the oscillator output. In this paper, the windowed harmonic is amplified by different magnification factors and then fed into the DVPO. The linear fitting relationship between the amplification factor and the PTAE is established, from which the absolute amplitude of the second harmonic is estimated. The simulations on aluminum plates with different sizes of contact microcracks validate that the PTAE can quantify the intensity of the second harmonic generated by contact microcracks. Moreover, the experimental data of aluminum plate also demonstrate that the proposed method can more accurately quantify the material nonlinearity in a noisy environment than other conventional denoising methods.

Here, a new three-dimensional graphene-carbon nanotube (3-D GR-CNT) structure was proposed, and the compressive mechanical properties and deformation behavior of the 3-D GR-CNT structure were evaluated using molecular dynamics (MD) simulations. It was found that the 3-D GR-CNT structure had outstanding mechanical properties, especially the ultrahigh Young's modulus, which was up to 1018 GPa and as high as that of GR. The 3-D GR-CNT structure did not have plastic deformation during the compression. The effects of GR length and CNT diameter were evaluated, and it was demonstrated that when the ratio of CNT diameter to GR length was about 0.6, the ultimate stress of the 3-D GR-CNT structure was the highest. Owing to the low density of the 3-D GR-CNT structure, the structure had outstanding specific strength. At a small compressive deformation, GRs produced buckling deformation with wrinkles to resist compression. After reaching the critical buckling stress, CNTs began to produce wrinkles; and after reaching the failure stress, the destruction started from the junctions. In addition, compared with the sp3 carbon atoms, the sp2 carbon atoms were more suitable for the junctions, as more energy could be absorbed by the sp2 carbon atoms in the junctions. Keywords: Three-dimensional graphene-carbon nanotube structures, Mechanical properties, Deformation behavior, Molecular dynamics

There are two severe limitations of current flexural wave metasurface based on local resonance mechanism or modal conversion method: low transmittance and only a single manipulation parameter. Inspired by the interaction between notches and flexural waves, we propose a high transmittance and multi-parameter independent manipulation metasurface composed of an array notches. Firstly, based on the phase shift accumulation method, a full 2π phase shift is achieved by modulating four notch parameters independently. Secondly, the refraction and focusing metasurfaces are designed based on the generalized Snell's law and compared with the simulation results. Finally, the designed focusing metasurfaces is validated by corresponding experiments. The four metasurfaces have a good performance for broadband flexural wave focusing, and the numerical and experimental focal lengths are in great agreement with the theoretical values. The notched metasurface provides an innovative way to manipulate flexural waves without resonators, which can be used in the applications of energy harvesting, waveguide design and ultrasonic detection.

We propose a novel method for locating and imaging contact delaminations in composite plates, using a network of PZT transducers and the nonlinear Lamb waves. Being immune to noise and sensitive to weak signal, the Duffing chaotic oscillator is utilized to detect the nonlinear harmonics of Lamb waves generated at the contact delamination interfaces. The Lyapunov exponent of the Duffing system output is calculated to quantify the relative intensity of nonlinear second harmonic. Its normalized value is taken as the damage index to locate and image the delaminations by combining with the probabilistic imaging algorithm. The numerical simulation study on the proposed method is performed. Compared with the nonlinearity parameter and the conventional damage index, the Lyapunov damage index (LDI) can image the single delamination or multiple delaminations more effectively, especially under the noise interference. The experiment using the LDI is also conducted on a composite laminated plate with multiple internal delaminations. The results show that the proposed imaging method based on LDI is also valid to the practical delaminations in the composite plate. It has the following advantages: immunity to noise, needlessness of baseline data, high imaging resolution and location accuracy.

The synergistic effects of surface treatment and interleaf on the interlaminar mechanical properties of glass fiber-aluminum laminates were studied. Aluminum sheets were treated with alkaline etching. Meanwhile, a graphene oxide (GO) interleaf was introduced between the aluminum sheet and the glass fiber-reinforced epoxy composite. Double cantilever beam and end-notched flexure tests were employed to evaluate the interlaminar fracture toughness of the glass fiber-aluminum laminates. The obtained results show that the toughening efficiency of the interleaf is dependent on the aluminum surface characteristics as well as the GO loading. Further comparison reveals that the highest mode-I and mode-II fracture toughnesses are obtained in the specimens with alkali etching treatment and addition of GO interleaf with 0.5 wt% of GO loading, which are 510% and 381% higher in comparison to the plain specimen. Fracture surfaces were observed to further uncover the reinforcement mechanisms.

In this work, a small pit on the internal surface of an aluminum thin-walled shell was inspected by using a technology of ultrasonic propagation visualization. This technology employs laser scanning within an inspection area to excite ultrasonic Lamb waves, and three cheap lead zirconate titanate (PZT) sensors to receive the wave signals. The laser scanning area and the three PZT sensors were located on the outside surface of the shell. Betti's reciprocal theorem was further incorporated into the present technology to visualize the wave propagation in the time-domain. The occurrence of notable scattering around the pit identified from the wave propagation snapshots at different time points can be used to detect the pit damage easily. We further adopted a method based on wave energy flow (WEF) map concept proposed by us to evaluate the size and shape of the pit. It was found that, even using a fast laser scanning of a step size of 8 mm, the present technology can still detect the damage quickly, and evaluate the damage accurately.

The existence of a closed micro-crack in plates can be detected by using the nonlinear harmonic characteristics of the Lamb wave. However, its location identification is difficult. By considering the transient nonlinear Lamb under the noise interference, we proposed a location identification method for the closed crack based on the quantitative measurement of Duffing oscillator transient transfer in the phase space. The sliding short-time window was used to create a window truncation of to-be-detected signal. And then, the periodic extension processing for transient nonlinear Lamb wave was performed to ensure that the Duffing oscillator has adequate response time to reach a steady state. The transient autocorrelation method was used to reduce the occurrence of missed harmonic detection due to the random variable phase of nonlinear Lamb wave. Moreover, to overcome the deficiency in the quantitative analysis of Duffing system state by phase trajectory diagram and eliminate the misjudgment caused by harmonic frequency component contained in broadband noise, logic operation method of oscillator state transition function based on circular zone partition was adopted to establish the mapping relation between the oscillator transition state and the nonlinear harmonic time domain information. Final state transition discriminant function of Duffing oscillator was used as basis for identifying the reflected and transmitted harmonics from the crack. Chirplet time-frequency analysis was conducted to identify the mode of generated harmonics and determine the propagation speed. Through these steps, accurate position identification of the closed crack was achieved.

The effects of recovery on the subsequent recrystallization of tantalum were investigated via two-step annealing at two temperatures. Transmission electron microscopy, electron back-scattered diffraction, and X-ray diffraction were employed to determine the respective microstructures and textures after various annealing regimes. The results show that many large grains with {111} orientations are developed when heating at 1573 K without pre-recovery, while pre-recovery can introduce a homogeneous fine microstructure and weaken the texture. This difference can be attributed to the recovery-induced change in nucleation mechanisms. Elongated grains stretch along grain boundaries or locate in the interior of deformed grains, mainly due to the heterogeneous distribution of stored energy. Dislocations characterized by submicron bands in the deformed state evolve into sub-grains during pre-recovery and grow continuously, indicating a homogeneous distribution of dislocation or stored energy after pre-recovery, which can significantly influence subsequent nucleation and grain growth.

The application of fiber-reinforced polymer (FRP) composites is gaining increasing popularity in impact-resistant devices, automotives, biomedical devices and aircraft structures due to their high strength-to-weight ratios and their potential for impact energy absorption. Impact-induced high loading rates can result in significant changes of mechanical properties (e.g., elastic modulus and strength) before strain softening occurs and failure characteristics inside the strain localization zone (e.g., failure mechanisms and fracture energy) for fiber-reinforced polymer composites. In general, these phenomena are called the strain rate effects. The underlying mechanisms of the observed rate-dependent deformation and failure of composites take place among multiple length and time scales. The contributing mechanisms can be roughly classified as: the viscosity of composite constituents (polymer, fiber and interfaces), the rate-dependency of the fracture mechanisms, the inertia effects, the thermomechanical dissipation and the characteristic fracture time. Numerical models, including the viscosity type of constitutive models, rate-dependent cohesive zone models, enriched equation of motion and thermomechanical numerical models, are useful for a better understanding of these contributing factors of strain rate effects of FRP composites.

To solve the problem that weak nonlinear Lamb waves caused by micro-cracks are often buried in background noises, a Duffing-Holmes system was used to enhance the weak nonlinear Lamb waves and the crack size was quantitatively characterized using Lyapunov exponent(LE). The frequency and amplitude critical threshold of the external driving force were determined according to the center frequency of excitation signal and the Poincare map of the Duffing-Holmes oscillator, respectively. After periodic extending and filtering, the Lamb waves were input to the Duffing-Holmes system, and then the nonlinear second harmonic was identified according to the phase trajectory and Poincare map. Based on the phase space reconstruction of Duffing system output, the maximal LE was calculated to characterize the magnitude of the second harmonic. Based on S0 Lamb wave mode, the simulations on models with different micro-crack sizes showed that the Duffing-Holmes system could accurately identify the structural micro-cracks under strong noise interference. Compared with the traditional acoustic nonlinearity parameter β ′ , the damage index defined here had a better linear relationship with the crack size, and the micro-cracks could be accurately quantified. The proposed method has obvious advantages for the detection of micro-crack defects under noise interference, and can greatly improve the sensitivity of nonlinear Lamb waves detection.

The area coefficients of thermal expansion (CTEs) of perfect single layer graphene sheet (SLGS) and SLGS with vacancy defects of different distributions were calculated in this work through molecul...

A remarkable synergetic effect between the graphene (GR) and carbon nanotube (CNT) in improving the interfacial mechanical properties of polyethylene polymer composites was investigated using molecular dynamics simulations. The reinforcement effects of two types of hybrid GR-CNT were evaluated. For the π−ππ−π stack hybrid GR-CNT, the alignment of CNT has a slight effect on the interfacial mechanical properties. For the covalent bond hybrid GR-CNT, the reinforcement effect increases with the CNT's length and radius, and multi-walled carbon nanotube is more efficient than single-walled carbon nanotube. With the same parameters of CNT, the interfacial mechanical properties of π−ππ−π stack hybrid GR-CNT is superior to the covalent bond hybrid GR-CNT. Compared with GR, the hybrid GR-CNT can effectively enhance the interfacial mechanical properties due to the synergetic effect between the GR and the CNT.

Mode-II interlaminar fracture toughness of GFRP/Al (aluminum) laminates is improved by employing acid treatment to an Al plate and inserting surface modified vapor grown carbon fiber (S-VGCF) between the Al plate and a GFRP layer. End notched flexure (ENF) tests are carried out to investigate the effect of S-VGCF addition on the Mode-II interlaminar fracture toughness. The experimental results demonstrate that the critical load and Mode-II fracture toughness of the specimen with acid treatment of Al plate and 10 g/m2 addition of surface modified VGCF are enhanced by 135.51% and 425.16%, respectively, compared to those of corresponding pristine specimen. Due to the presence of the oxygen containing functional groups, the specimens with addition of S-VGCF possess much higher Mode-II fracture toughness compared to the specimens with addition of pristine VGCF. Laser scanning and scanning electron microscopies are employed to observe the fracture surface of specimens to reveal the improvement mechanisms. Moreover, numerical simulations are performed based on the cohesive zone model to verify the experimental results. The interfacial shear strength between the Al plate and the GFRP layer are also predicted by the numerical simulations.

A pulse laser combined LWT technique with a two-stage reconstruction algorithm was proposed to realize rapid damage location, or even the evaluation of damage size for plate-like structures. Since the amplitude of Lamb waves in propagation is highly sensitive to damage, including inside damage, the change of the attenuation coefficient of Lamb waves in the inspection region was used as a damage index to reconstruct damage images. In stage one, the rough area of the damage was identified by a comparison of the amplitude of the testing signal data and reference data (undamaged state). In stage two, the damage image was reconstructed using an inverse approach based on the least-square method. In order to verify the effectiveness of the proposed rapid approach, experiments on an aluminum plate with a non-penetrating notch and a carbon fiber-reinforced plastic laminated plate with internal delamination induced by a low-velocity impact were carried out. The results show that the notch can be detected with accurate location, and the delamination image can be reconstructed successfully.

Enhancing thermal energy transport is critical for the applications of 2-dimensional materials. Here, we explored the methods of enhancing the interfacial thermal energy transport across the graphene (GR)/hexagonal boron nitride (h-BN) heterostructure interface, and revealed the enhancement mechanisms of interfacial thermal energy transport by applying non-equilibrium molecular dynamics (NEMD) simulations. The computational results indicated that both doping and interface topography optimization could effectively improve the interfacial thermal conductance (ITC) of the GR/h-BN heterostructure. In particular, the enhancement of the zigzag interface topography led to a much better result than the other methods. Doping and interface topography optimization increased the overlap of the phonon density of states (PDOS). Temperature had a negligible effect on the ITC of the GR/h-BN heterostructure when the temperature exceeded 600 K.

Fluorescent europium-doped nanohydroxyapatite (Eu-nHA, 5 at.% Eu) was prepared by a precipitation method followed by annealing at 600 °C. Transmission electron microscopy and X-ray diffraction analyses reveal the nanocrystalline nature of the annealed Eu-nHA particles, which are 20–40 nm in width and 40–60 nm in length. Elements of Ca, P, O and Eu are detected by energy dispersive X-ray analysis. Upon excitation by 250 nm ultraviolet light, the annealed Eu-nHA (Eu-nHAa) nanoparticles display strong pinkish-red luminescence in the fluorescence spectrum. Moreover, the Eu-nHAa powder shows green and red colours by the irradiations of blue and green lights, respectively. The in vitro cell proliferation assessment and the lactate dehydrogenase activity assay indicate that the Eu-nHAa nanoparticles with the concentrations of 0.3, 3 and 30 μg/ml have inhibitory effects on human umbilical vein endothelial cells in a dose- and time-dependent manner. The fluorescent Eu-nHAa nanomaterial would have potential applica...

A series of graphene (GR) pull-out simulations based on molecular dynamics (MD) were carried out to investigate the interfacial mechanical properties between GR and a polymer matrix (polyethylene: PE). The effects of pull-out velocity, number of vacancy defect in GR and temperature on the interfacial mechanical properties of a GR/PE nanocomposite system were explored. The obtained results showed that the pull-out velocity and the temperature have significant influences on the interfacial mechanical properties for a perfect GR. Moderate vacancy defects in GR can effectively enhance the interfacial mechanical properties in GR-based polymer nanocomposites.

The interfacial mechanical properties between graphene (GR) and a polymer matrix play a key role in load transfer capability for GR/polymer nanocomposites. Grafting of polymer molecular chains on GR can improve the dispersion of the GR in a polymer matrix and change the interfacial mechanical properties between the GR and the polymer matrix. In this work, we investigated the interfacial mechanical properties between GR functionalized with polymer molecular chains and a polyethylene (PE) matrix using molecular dynamics simulations. The influences of grafting density and chain length on the interfacial mechanical properties were analyzed. The results show that grafting of short PE molecular chains on GR can significantly improve the interfacial shear strength and interfacial Mode-II fracture toughness in functionalized GR/PE nanocomposites.

Flexible ultrasensitive piezoresistive strain sensors were fabricated by CO2 Laser ablating of the surface of the multiwall carbon nanotube/polydimethylsiloxane (MWCNT/PDMS) composite film prepared by a coating process. The effects of the MWCNT content and the applied laser power on the electrical and sensing performances of the MWCNT/PDMS composite strain sensor were systematically investigated. It is found that, after laser ablating, the electrical conductivity and the sensing gauge factor of the MWCNT/PDMS film were greatly improved only by the addition of 1.0 wt% of MWCNT, which is below the percolation threshold of the MWCNT in the PDMS matrix. A novel boscage-like structure at the surface of the film formed by the ablation of the PDMS and the rearrangement of the MWCNT during the laser ablating process was found responsible for the ultrahigh gauge factor of the composite strain sensor, which is about 513 at the strain of 5.0%. The facile and cost-effective fabrication process of the flexible ultrasensitive strain sensor could be simply extended to other polymer composites for the development of new multifunctional and wearable electronic devices.

Controlling wave propagation is a popular research field; however, progress with regard to the study of elastic waves is slow because of the coupling of different types of waves. In this paper, we report a novel approach to design elastic metasurfaces for controlling elastic shear vertical (SV) waves in solids. The metasurface is composed of separate parallel thin plates connected at both ends to half-space solids. The elastic SV-waves in solids were controlled by manipulating the induced flexural waves in the thin plates of the metasurface. Based on the form invariance of the governing equation for flexural waves in a thin plate under linear coordinate transformations, the uniaxial scaling transformation method (USTM) has been put forward to alter the material to constitute the thin plates of the metasurface. The transformed material is transversely isotropic, which greatly reduces implementation difficulties. To tune the traveling times of the flexural waves in the thin plates, different values of the scaling parameter α and plate thickness h were assigned for different thin plates based on the Kirchhoff plate theory. By combining the plate thickness variation approach with the USTM, the plate length of the metasurface could be effectively controlled to be smaller than the wavelength at the working frequency. To demonstrate the performance of the proposed approach, two designs of elastic metasurfaces for wave focusing and abnormal refraction were described in detail, and full numerical simulations were conducted. The present approach opens a promising avenue toward the realization of metasurfaces for controlling elastic waves.

This paper investigates the propagation of low-frequency S0 mode Lamb waves in plates with quadratic nonlinearity through numerical simulations and experimental measurements. Both numerical and experimental results manifest distinct ultrasonic nonlinear behavior which is mainly presented by the second harmonics. Meanwhile, we find that both the acoustic nonlinearity parameter and dispersion distance show the exponential decay trend with the increase of frequency-thickness. Moreover, the results reveal that the frequency is key to affect the acoustic nonlinearity parameter and dispersion distance with the same frequency-thickness. This study theoretically and experimentally reveals that nonlinear Lamb waves of the low-frequency S0 mode are feasible to quantitatively identify material weak nonlinearity in plates.