Nonlinear Damage Research Articles

Numerical collapse simulation based critical state analysis for framed‐wall structure subjected to earthquakes

SummaryWith the rapid developments of the constitutive theory, numerical methods, and computer software and hardware, full attention has been paid to establishing nonlinear structural models and investigating the nonlinear behavior, damage performance, and failure criterion of the structures. Consequently, this study introduces a precise analysis with a highly accurate level of simulation for an existing framed‐wall structure excited with strong ground motions. The incremental dynamic analysis (IDA) technique has been adopted to investigate the nonlinear behavior of the structure. The damage evolution and collapse pattern have been well captured in the structure based on the adopted damage model. The results showed that the maximum interstory drift (ISD) position varies at different seismic loads due to the damage initiation and propagation variation. The IDA curves show the end of the elastic stage at 0.70, 0.50, 0.70, and 0.20 g at San Francisco, Italy, Northridge, and San Fernando ground motions, respectively. Also, different collapse patterns of the structure have been observed at different ground motions and also at different intensities for the same ground motion. Therefore, the high‐rise building design should account for multiple collapse patterns. Moreover, a new IDA‐based technique is proposed to estimate the structure's maximum seismic capacity (MSC) and ensure it through the collapse analysis. The structure adopted in this study reaches its MSC at the San Francisco event at an intensity of 2.50 g. However, the MSC decreased by 40% at Italy and Northridge events and 60% at the San Fernando event. Since the seismic capacity of the structure is considered an essential ingredient in the design process, therefore, the findings of this study are supposed to lay the basis for the performance‐based seismic design of the structure.

Grain-based modelling of dynamic shear rupture of heterogeneous rock using a coupled continuum-discrete model

Dynamic shear rupture of rocks plays a significant role in the formation of earthquake faults and the stability of underground engineering structures at depth. This paper aims to explore shear strength, progressive fracturing and seismicity, and underlying shear failure mechanisms of heterogeneous rock under dynamic loads. A lab-scale direct shear test is conducted on a cubic granite sample by using a Triaxial Hopkinson bar (Tri-HB) system, and a coupled continuum-discrete element method is applied to simulate the functionality of the full-scale Tri-HB system for dynamic direct shear tests. The evolution of shear stress and strain distribution shows obvious concentration around the shear rupture band, which verifies the feasibility of the designed testing and modelling configuration for characterising dynamic shear stress and deformation. A grain-based discrete element method (GB-DEM) is adopted to represent the mineralogical heterogeneity of granite and to reveal multi-scale fracturing and seismic activities under dynamic shear loads. The microcracking process shows a transition of the dominant failure mode from intergranular crack to transgranular crack during the shear process. The shear rupture zone is typically initiated from the discrete fractures inclined at certain angles, which are gradually coalesced to form a main shear fracture that breaks the rock into two main blocks. The seismicity of the shear rupture process shows a drop in the b-value before the peak shear stress, followed by a certain degree of recovery at the post-failure stage. We found that shear mechanical response and rupture behaviour show a strong dependency on both strain rate and initial normal stress. The number of transgranular cracks is increased with increasing strain rate, which consequently results in intensively crushed mineral grains. Inclined fractures become steeper under higher initial normal stresses which further widen the shear rupture band. The normal-shear stress curves show a common trend of two linear increase stages followed by nonlinear damage and failure processes. The shear strength can be approximated by the Mohr-Coulomb strength envelope under various initial normal stresses and strain rates.

A non-linear cohesive zone model for low-cycle fatigue of quasi-brittle materials

The low-cycle fatigue behaviour of quasi-brittle materials (e.g., concrete and rock) that is characterized by fatigue induced inelastic deformation significantly affects the integrity and serviceability of engineering structures. However, the low-cycle fatigue mechanism and fatigue-controlled fracture process of quasi-brittle materials is not clear. This paper develops a new cyclic cohesive zone model (CZM) for low-cycle fatigue of quasi-brittle materials. Based on in-situ stress and damage state, a nonlinear fatigue damage model is proposed and implemented into the cyclic CZM. The fatigue parameters are determined based on S–N curve. A worked example for monotonic and cyclic loading of concrete beam under three-point bending is presented to demonstrate the application of the developed numerical model. After validation against experimental data, the fatigue crack mechanisms are discussed and a comprehensive parametric study is carried out to investigate the effects of fatigue parameters, stress levels and loading sequences on the fatigue failure. It has been found that there are three stages for the development of crack mouth of displacement, i.e., crack initiation, stable growth and rapid fracture which are caused by combined static and fatigue damage, fatigue damage, and combined static and fatigue damage dominated by static damage, respectively. The developed cyclic CZM is practically significant and its parameters are easy to be determined based on S–N curve. It provides a new and useful tool for low-cycle fatigue crack modelling of quasi-brittle materials.

Deformation Mechanics of Fuel Cell Gas Diffusion Layer: Cyclic Response and Constitutive Model

The deformation mechanics of a typical gas diffusion layer using experimental and advanced modelling technique is reported. The experimental cyclic response is observed similar to pseudo-elastic materials with highly nonlinear loading/unloading. The cyclic compressive mechanical response of gas diffusion layer (GDL) is modelled to be the outcome of cumulative changes in deformation kinematics of matrix and fiber fractions. The individual mechanisms necessitating the energy dissipation, residual strain, and stress softening during cyclic mechanical response are related to nonlinear hyperelastic matrix with the damage function and inelastic activation function at the interface of constituents. The model predicts highly nonlinear elastic loading, residual strain, hysteresis, and damage quotient associated with stress softening as a function of several cycles. The significant takeaway from this study is in terms of quantifying strength, inelastic nature of individual constituents. The proposed model is simulated for low-level altering stresses of up to twenty cycles. The results show the build-up of residual strains and hysteresis as a function of fuel cell clamping pressure.

Characterization of strength, modulus, and fatigue damage properties of cement stabilized macadam based on the double modulus theory

• Flexural tensile strengths calculated with tensile and compressive differences are reduced by nearly 20 % when compared to those calculated without tensile and compressive differences. • A power function decay model of the tension–compression moduli of cement stabilized macadam was established in the four-point bending fatigue test. • The fatigue damage model of cement stabilized macadam was established and its accuracy was verified. Cement stabilized macadam (CSM) is a mixture created by combining cement as a binding material, water, and various particle sizes of minerals. The cement stabilized macadam material exhibits different moduli in tension and compression due to both its mechanical properties and the mechanical response in the asphalt pavement structure. To explore the strength, modulus and fatigue damage characteristics of CSM under different tensile and compressive modulus, this paper carried out the research. The calculation formulas for flexural tensile strength and tension–compression modulus were derived based on the difference in tension–compression modulus. A four-point bending strength test of CSM was carried out. Four-point bending fatigue tests with varying stress ratios were performed. It reveals deterioration laws of tension–compression modulus during fatigue process. The double logarithmic fatigue equation of CSM, as well as its nonlinear fatigue damage evolution equation, are established based on fatigue life results. The results of an analytical solution for fatigue life of rectangular section beams based on damage mechanics were obtained and compared to the results of four-point bending fatigue tests. The results reveal that the modulus of CSM differs in tension and compression. The calculated flexural tensile strength with the tension and compression difference is nearly 20 % lower than without the difference. The calculation approach that does not account for the difference in tension and compression overestimates the flexural tensile strength of CSM. The tension–compression moduli of CSM exhibit a power function decay law in the four-point bending fatigue processes. In the first stage, the dynamic modulus decays at a steady rate, accounting for 90 % of total fatigue life. The second stage in the life ratio of 0.9 occurs when the decay rate of the modulus rapidly increases and enters the stage of sharp decay. Based on the results of the four-point bending test, the modulus decay model was created. The decay parameter m has an exponential relationship with the stress ratio. The relative errors between the mean values of fatigue life tests and the predicted values of the analytical solutions range from 10.8 to 30.6 percent. The established fatigue damage equation for CSM can better reflect its fatigue damage evolution law. The research findings have great significance to solve the determination of pavement materials parameters based on the difference in tension and compression modulus. It also has a specific reference value for asphalt pavement design theory and calculation method when the varied modulus of tension and compression are considered.

Nonlinear analysis of reinforced concrete slabs under high-cyclic fatigue loading

Infrastructures are frequently vulnerable to sustained cyclic loads and structural vibration. The accumulated cyclic stresses will induce fatigue in the structures and contribute to their inadequate service lifespan. Consequently, analyzing the present structural health status by the structural stiffness measurement is crucial. This study investigated the fatigue performance and dynamic progressive damage behavior of reinforced concrete (RC) slabs under high-cyclic fatigue loadings using nonlinear finite element (FE) analysis. A new model was recommended for predicting the concrete's residual strength. The accuracy of the suggested model and the FE simulation was validated by comparing the predicted natural frequencies, mode shapes, residual strength, and crack characteristics of specimens with the experimental results. Finally, a novel model for determining the dynamic stiffness of RC slabs was developed. Results showed that the cumulative degradation of the natural frequency, stiffness, and damage development of steel rebars and concrete increased as the fatigue loading cycle increased, indicating that the dynamic response and fatigue damage for RC slabs in the later stages of high-cyclic fatigue loading were more severe. Additionally, the RC slab's natural frequency was reduced rapidly during the initial steps of fatigue and, after that, slowed noticeably. Validation of the dynamic stiffness model demonstrated its capability in predicting the stiffness of fatigued and damaged RC slabs. The results provide practical insights for analyzing the dynamic behavior of existing structures by considering the nonlinear progressive damage and may improve the efficiency of structural damage detection.

A three-dimensional nonlinear rock damage creep model with double damage factors and residual strength

A three-dimensional nonlinear rock damage creep model with double damage factors and residual strength

Star Crack Formation via Low-Velocity Impact on Glass Windows

The resistance to crack formation induced by gravel impacts on laminated glass windshields is a crucial issue for windshield manufacturers. It is proposed to study the star crack formation on polyvinyl butyral (PVB) laminated glass by designing a new highly-instrumented device that can break the glass under dynamic loading. The set-up is composed of a spring-loaded projectile that mimics a gravel momentum and an input bar equipped with strain gauges, whose end is an indenter initially in contact with the laminated glass sample. A synchronized high-speed camera allows for the observation of the crack growth. A unidimensional model introduces the local non-linear behavior of the indented zone. Crack monitoring synchronized with the Force and Velocity measurements are presented. Live-indentation depth measurements are performed. Experimental results are used in a dynamic simulation to analyze the non-linear damage behavior under the indenter tip. Dynamic and well-instrumented indentation experiments on the laminated glass are performed to investigate the star-shaped crack formation and describe the indented zone. This work is a prelude to the crack length prediction on windshields submitted to gravel pitting.

Temporal Contrast Enhancement Based on the Self-Diffraction Process with Different Kerr Media

In this study, the self-diffraction (SD) process proved to be a competitive method to achieve a seed pulse with high temporal contrast in ultra-intense lasers. Several different nonlinear, transparent Kerr media including BK7 glasses, AL2O3 and CVD diamonds were compared experimentally to obtain SD signals with high energy and high conversion efficiency. AL2O3, with a high third-order nonlinear coefficient and high laser damage threshold, was found to be the best medium to improve the conversion efficiency of SD signals. The highest first-order SD signal of 401.7 μJ was achieved, with the conversion efficiency at approximately 9.1%, when the incident pulse energy was 4.40 mJ. The temporal contrast of the obtained first-order SD signal was improved by 7 orders of magnitude to 1012. As a result, this cleaning pulse will facilitate research involving ultra-intense laser systems and high-intensity laser–matter interactions.

Structural nonlinear damage identification based on Bayesian optimization GNAR/GARCH model and its experimental study

Cracks and bolt looseness are common damages in a steel structure. Under the time-history loading, nonlinear characteristics of variable stiffness exist in cracks, and bolt looseness has complex nonlinear characteristics of stiffness and damping. To effectively solve the problem of structural nonlinear damage identification, an output-only damage identification method based on the GNAR/GARCH (general expression for linear and nonlinear autoregressive/general autoregressive conditional heteroskedasticity) model with Bayesian optimization is proposed. First, the stationarity test and continuous difference processing was carried out on the measured acceleration data, and an order determination method based on Bayesian optimization was proposed to automatically select the optimal model order. Then, a model structure optimization method based on Bayesian optimization was proposed to select the optimal model structure of a GNAR/GARCH model, and a GNAR/GARCH model was established based on the measured acceleration data for damage identification. Finally, a new damage indicator PIDI (probabilistic Itakura distance indicator) was proposed to judge the structural healthy status. The nonlinear damage experiment of three-story frame and relay tower was used to verify the effectiveness of the proposed method. In addition, in order to illustrate the efficiency of the proposed method for nonlinear damage identification, a comparative study was carried out using other two damage identification methods. The results show that the nonlinear damage identification method based on the GNAR/GARCH model with Bayesian optimization can easily identify the nonlinear damage of the frame and relay tower structure, and it can effectively identify the structure damage with single or multiple nonlinear damage sources.

Optical damage and the third-order nonlinearity in GeGaS glasses

We have measured optical properties of GexGa4S96-x (x=22.5, 27, 30, 33.3 and 36) glasses including optical bandgap Eg, hardness, linear and nonlinear refractive index and laser damage threshold. We found that, both Eg and laser damage threshold exhibit maximum values in Ge30Ga4S66 glass, linear refractive index increases with increasing Ge content, but nonlinear refractive index has a minimum in Ge30Ga4S66, and their correlation can be well described by the Miller’s rule. We conclude that, Ge30Ga4S66 glass with chemically stoichiometric composition might be ideal for the chalcogenide-based optical amplifiers since it has reasonable optical nonlinearity, and high figure of merit (FOM) and laser damage threshold.

An event-oriented reliability assessment for DC link capacitors in grid connected inverter with low voltage ride through operation

Low voltage ride-through (LVRT) capability has been standard into the operating specifications of grid-connected inverters in many countries. Due to the mismatch of the time scale and lack of stress description model under the LVRT operation, the traditional mission profile reliability analysis tools are difficult to be applied for capacitors under LVRT operation. To overcome the above issue, this paper analysis the electrical and thermal stress of the DC link capacitors under LVRT operation, and established a lifetime model for the LVRT operation by the accelerated aging test. An extended mission profile and a nonlinear damage accumulation model have been proposed to evaluate the impact of the LVRT event on the reliability of DC link capacitors. A reliability assessment has been conducted for a 7.5 kW inverter which experienced one LVRT incident as an analytical example.

Characteristic of fixed abrasive polishing for KDP in an anhydrous environment.

High grade optical components are rapidly being employed in a wide range of applications due to their great performance. Among these, KDP (potassium dihydrogen phosphate) is the preferred choice for frequency doubling components because to its large non-linear optical technique and high laser damage threshold. In this research, KDP is treated employing fixed polishing in an anhydrous environment. Copper oxide is utilized as abrasive, and toner and phenolic resin are combined to form pellets for KDP polishing. Calculation of the temperature field on the surface of the workpiece based on the relationship of the movement. The ideal polishing parameters are also determined from the findings of the temperature field and the optimum process parameters are 5kPa pressure, 150rpm and 8mm eccentricity. A new material removal model is presented and based on this, a unique processing technique to increase the material removal depth is provided. Interestingly, with this form of polishing, the surface roughness of the workpiece remains about Ra 20nm after a quick shift and does not alter with re-pressing.

Nonlinear Energy Evolution Characteristics of Diorite Examined by Triaxial Loading-Unloading and Acoustic Emission Tests.

Acoustic emission (AE) is often accompanied by the propagation of internal microcracks in loaded rock samples, and it essentially reflects microinstability phenomena driven by energy redistribution under stress. In this paper, loading and unloading tests were carried out to investigate the internal nonlinear damage evolution characteristics of diorite samples under different unloading confining-pressure rates. The nonlinear mechanical characteristics of the strain energy sequence of diorite were studied by applying nonlinear dynamics and basic chaos theory and MATLAB software. Moreover, the evolution characteristics of AE counts and AE energy of rock samples were investigated, and their microcrack-propagation modes were analyzed based on the RA–AF scatter distribution of AE and a two-dimensional Gaussian mixture model. Finally, according to the evolution characteristics of energy and AE, the nonlinear damage evolution mechanism of diorite under loading and unloading conditions was revealed. The results show that, before the loading and unloading peak strength, when the strain-energy-promotion coefficient, r, is equal to 1 or changes in the ranges of 1–3, 3–3.57, and ≥3.57, the strain-energy evolution of diorite presents the characteristics of supercritical stability, nonlinear stability, period-doubling stability, and chaos, respectively. Meanwhile, the greater the rate of the unloading confining pressure, the earlier the period-doubling bifurcation and chaotic mechanical behavior will occur. After loading and unloading peak strength, the sudden decrease of high-density AE counts and AE energy or the sudden transition of the strain-energy-promotion coefficient from >0 to <0 can be used as an important criterion for the complete failure of rock samples.

Comparison of sensitivity in nonlinear ultrasonic detection based on Lamb wave phase velocity matching mode

ABSTRACT In nonlinear ultrasonic damage detection, the appropriate Lamb wave mode to accurately characterise the nonlinearity attributed to the material damage should be selected important. However, an effective mode is more difficult to select practically as impacted by the dispersion and multi-mode characteristic of the Lamb wave. In this study, based on the dispersion curve of Lamb waves, the modes meeting the second harmonics and third harmonics phase velocity matching were given, and the nonlinear cumulative effects exerted by different modes on fatigue cracks were compared. In addition, an investigation was conducted on the amplitude change of the second and third harmonics signal of the identical fatigue damage. The results show that the harmonic amplitude decreases with the increase of the fatigue crack length. The third harmonics under the two modes are more sensitive to fatigue damage than the second harmonics. Moreover, the amplitude of the third harmonic excited by S1 mode exceeds that of the other mode. As the fatigue crack length increases, the relative second- and third-order nonlinear coefficients generated by S1 mode have approximately the same trend, first increasing and then decreasing. The results reveal that the third harmonic under S1 mode could more effectively characterise fatigue damage.

Nonlinear Electro-Mechanical Impedance Spectroscopy for fatigue crack monitoring

This article presents a Nonlinear Electro-Mechanical Impedance Spectroscopy (NEMIS) methodology for fatigue crack monitoring. Different from the conventional Electro-Mechanical Impedance Spectroscopy (EMIS) implemented in the frequency domain, the proposed NEMIS employs a temporal chirp interrogating signal to obtain the impedance spectra, and simultaneously captures the Contact Acoustic Nonlinearity (CAN) features. To develop an insight into the mechanism behind the NEMIS method, a comparative investigation between the conventional EMIS and the two-phase NEMIS algorithm was conducted. Numerical studies were carried out on a 1-D transitional-bilinear CAN model to demonstrate the chirp-induced higher harmonics and nonlinear mixed-frequency response features. Furthermore, finite element (FE) simulations were conducted to demonstrate the feasibility of the NEMIS. A baseline-free damage index was subsequently developed to quantify the severity of the fatigue crack. Finally, experimental validation of the NEMIS method was performed. The experimental results validated the feasibility and accuracy of the chirp-based impedance spectra. It was also shown that NEMIS successfully captured the nonlinear impedance spectra, obtaining higher harmonics and wave modulation features to manifest the existence of the fatigue crack. Quantification on the severity of the crack was conducted via the nonlinear damage index, which presented a consistent, monotonic trend with the increasing severity of the fatigue crack. The experiment demonstrated the capability of NEMIS for detecting and quantifying fatigue cracks. The article finishes with summary, concluding remarks, and suggestions for future work.

Nonlinear mechanical characteristics and damage constitutive model of coal under CO2 adsorption during geological sequestration

Geological sequestration of CO2 is an effective way to achieve the goal of reducing global warming and carbon neutralization. The complex CO2–coal interaction will lead to the change of mechanical properties of coal. Therefore, evaluating the mechanical characteristics of deep coal seam after CO2 adsorption is of great significance for analyzing the geological characteristics and structural stability of deep strata and storage site selection. In this study, the triaxial compression test and acoustic emission (AE) test were used to evaluate the effect of CO2 adsorption pressure on the mechanical properties of coal mass. On the basis of the evolution characteristics of AE ring down count (RDC), fractal theory was used to analyze the deformation and fracturing evolution of coal. Besides, an elastic damage constitutive model describing the nonlinear stress-strain relationship of coal under CO2 adsorption is established. Results show that the growth of adsorption pressure develops the risk of damage and fracturing of coal. With the increase in adsorption pressure, the value of singularity index width Δα presents a downward trend, indicating the development of internal cracks and the increase in the complexity of microunit fracturing process. When the adsorption pressure is low, the gas in large cracks and pores leads to the generation of small AE signal that occupies the dominant position. High adsorption pressure increases the complexity and nonlinearity of coal deformation, strengthens the proportion of large AE signal, and leads to the increase in the average value of multifractal spectrum width Δf. With the increase in adsorption pressure, the fracturing degree of coal is higher, a mass of large-size cracks appears, and more AE spectrum presents intensive distribution. In the plastic stage, the load level is close to the strength limit, the microcracks intersect with each other, and the average value of Δα in this stage is the smallest.

Origins of THz Modes and Their IR Intensities in LiNbO3

LiNbO3 crystals have been essential materials for generating freely propagating terahertz (THz) pulses among other materials because of their excellent nonlinear optical properties and high damage thresholds. However, one of their dielectric properties─the huge IR intensities of THz modes─has been impeding their practical applications. Such IR intensities produce additional contributions to the refractive index, making the phase-matching between the optical pump and THz radiation difficult. The large IR intensities also lead to strong THz absorptions, reducing the conversion coefficient. Although a couple of techniques have been applied to solve or avoid the relevant problems, a more fundamental question regarding the atomic mechanism of generating the huge IR intensities of THz modes in LiNbO3 has not been discussed so far. We performed a rigorous analysis of the nature of THz modes in terms of the contributions from the constituent atoms Li, Nb, and O using a quantitative approach originally developed in the previous studies. We further clarified the roles played by the motions of the constituent atoms in generating IR intensities by calculating the associated Born charge vectors. We revealed that the librations of the O octahedra, despite their prominent presence in some THz modes, are IR-silent motions. The translations of the O octahedra and Nb cations are the leading contributors to IR intensities, while the internal vibrations of the O octahedra play a destructive role. We propose two mechanisms for reducing the IR intensities of THz modes in LiNbO3 based on the analyzed results.

Random fatigue life prediction of automobile lower arm via modified Corten–Dolan model

AbstractThe fatigue life for the rear suspension lower arm of the passenger car is investigated. The road load signals collected by the sextant force measuring instrument are processed. And the frequency histogram of it is plotted and its distribution characteristics are analyzed. The load signal is extrapolated to a cumulative frequency of 106 using the parametric method, and the one‐dimensional load spectrum of the lower arm is compiled. Based on the nonlinear fatigue cumulative damage theory, Corten–Dolan model is modified by introducing the kth power of the stress ratio between two adjacent levels. The improved fatigue life prediction model is established and the validity of the model was determined by experimental data. And the improved Corten–Dolan and the linear cumulative damage model are used to predict the life of the lower arm under one‐dimensional load spectrum respectively.

Method for statistical evaluation of cumulative damage models applied to block loading

AbstractThere is an abundance of nonlinear fatigue damage accumulation models but a lack of verification and comparison to experimental datasets. First, an extensive two‐level block loading experimental fatigue dataset is reprocessed according to current standard practice. Next, four nonlinear damage accumulation models and the Palmgren–Miner linear damage rule are critically compared using a range of statistical metrics. For the considered dataset, the Palmgren–Miner rule consistently performs worst and the damage curve approach is found to perform significantly better than the other nonlinear models. This study shows that the current practice of performance verification of new fatigue damage accumulation models in literature is too limited which enables cherry‐picking of verification datasets to improve perceived performance. Future fatigue damage accumulation models should be verified much more rigorously to both readily available and new experimental datasets.