Nonlinear Damage Research Articles

Quantitative damage evaluation of tunnel subjected to a subsequent strong seismic after a quasi-static reverse faulting

An individual fault dislocation or seismic effect is often considered to investigate the deformation and failure of a fault-crossing tunnel, while emerged in high-intensity seismic zones, it will be likely to subject to a superimposed effect from fault dislocation and strong seismic excitation. In this study, a three-dimension numerical model to simulate fault dislocation and subsequently dynamic response characteristics of fault-crossing tunnel was established, in which fault dislocation and earthquake levels at the site of interest. The nonlinear damage feature of tunnel was considered to furtherly reveal damage states of tunnel under the superimposed effect. And then, a quasi-static large-scale model test was performed to verify the correctness of pre-order fault dislocation calculation results. The results showed that only when the tunnel was subjected to fault dislocation, a prominent relative deformation of tunnel exists in the fault fracture zone and tension and compression zone were noticeably identified at the convex and concave zones respectively. After superimposing the seismic loading, acceleration and equivalence plastic strain amplification of tunnel near the fault fracture zone is great of significance and the damage of the tunnel under the fault dislocation was concentrated at the fault core. More importantly, the fault-crossing tunnel is more of sensitivity to the initial fault dislocation from the obvious rising on the tension damage index, and when PGA is greater than 0.2 g, the tunnel emerged in the host rock mass should also be paid more attentions, not only the tunnel in the potential fault-affected zone.

Experimental study on failure characteristics and rheological properties of pillar-like rock samples with different shapes

The stability of coal pillar is extremely important to the control of rock strata movement and surface subsidence. It is of great significance for mining design to analyze the stability and failure characteristics of coal and rock pillars left after mining and to study the failure characteristics and rheological properties of coal and rock with different shapes. In this paper, based on uniaxial compression and rheological tests on rock samples, the rheological properties of rock samples with different shapes were discussed by using the nonlinear theoretical mechanics and damage theory, and the rheological mechanical characteristics of coarse yellow sandstone samples under the action of different free surface areas and the same loading contact area were investigated by means of experimental research, theoretical analysis and numerical simulation. The following conclusions were drawn: the failure characteristics and dynamic change process of rock samples with different shapes under the same loading contact area are obtained by uniaxial compression test and multi-stage rheological loading. The uniaxial compressive strengths of rock samples with the same loading contact surface area and different free surface areas are inversely proportional to their free surface areas. For the round sample, the stress level in the rheological test is obviously lower than the instantaneous peak uniaxial compression strength, while for the other samples, the stress level in the rheological test is close to the instantaneous peak uniaxial compression strength. For rock all these samples, both the ratio of steady-state rheological time to final failure time and the deformation degree decrease with the increase of free surface area.

Nonlinear seismic response and damage evolution of a mountain tunnel: Multi-scale simulation by IBEM-FEM coupled method

Studying dynamic response and damage assessment of mountain tunnels is paramount in earthquake engineering. This paper proposed a novel method, the indirect boundary element method-finite element method (IBEM-FEM) coupled method, aimed to concurrently simulate the amplification effect of kilometer-scale mountain topography and the damage evolution in a centimeter-scale lining tunnel section. The proposed method involves two fundamental steps. Initially, the input motion on the truncation boundary within the mountain is accurately determined using the indirect boundary element method (IBEM). Subsequently, the nonlinear dynamic behavior of the tunnel structure and its adjacent area is analyzed by the finite element method (FEM) based on the results from the previous step. This study numerically simulates the seismic damage and failure mechanisms of a mountain tunnel considering three influence factors: incident wave types, incident wave intensities, and surrounding rock mass grades. The results indicate that mountain topography amplifies the seismic response, thereby affecting the dynamic behavior of the tunnel. Under the incidence of SV-waves and P-waves, the dynamic damage distribution patterns of the tunnel lining are significantly different. Moreover, as seismic wave intensity increases, the peak values of tunnel stress exhibit a non-monotonic increasing trend. The surrounding rock mass grade also significantly affects the dynamic response and damage distribution of the mountain tunnel. Overall, the proposed IBEM-FEM coupled method can effectively consider complex mountain topography and is applicable for evaluating the nonlinear seismic response of mountain tunnels.

Strain-controlled creep-fatigue interaction property of Nb521 refractory alloy: Hold time effect and life prediction

Strain-controlled creep-fatigue interaction (CFI) tests were conducted for NbW alloy, i.e., Nb521 alloy, at 900 °C with a strain amplitude of ±0.3% under atmospheric conditions to study the effect of hold time on the CFI failure behaviour, with the results indicating that the creep-fatigue life of the Nb521 alloy decreased with an increase in the hold time. The decline rate gradually flattened, with no saturation effect observed. Furthermore, with an increase in the hold time, the hardening rate of the Nb521 alloy gradually decreased, but the softening rate remained high. Fatigue fractures can be divided into stable propagation, rapid propagation, and final fracture zones according to their morphological characteristics. Compared with the stable propagation zone of the pure fatigue fracture surface, the creep damage caused by the hold time resulted in numerous intergranular fracture features in the stable propagation zone of the CFI fracture surface, indicating that the crack propagation mode changed from a transgranular fracture to a mixed transgranular–intergranular fracture. The strain energy density exhaustion model under nonlinear damage summation better reflects the CFI damage behaviour, with the creep-fatigue life prediction result considered acceptable.

A quantitative monitoring method for the pretightening state of bolts based on nonlinear Lamb waves and incremental learning

ABSTRACTThe degradation of the pretightening state of bolts is a multistage process. Utilising a single model to monitor the pretightening state in the full degradation stage and continuously updating the monitoring model is important. Therefore, a quantitative monitoring method for the pretightening state of bolts based on nonlinear Lamb waves and incremental learning is proposed. In the proposed method, phase reversal technology is first adopted to enhance the sensitivity for bolt loosening, and then a relative nonlinear coefficient based on phase reversal (RCP) is constructed. The disadvantage that linear indicators are insensitive to early loosening is overcome and the critical points of the multidegradation process are identified by this indicator, the tight contact stage (TCS) and the significant loosening stage. After the TCS is determined, a quantitative monitoring model, which fuses seven nonlinear damage indexes, is established based on incremental canonical correlation forests (ICCF). This algorithm achieves incremental learning by continuously increasing the number of decision trees. To verify the effectiveness of the method, an experimental study is carried out on four bolts. The monitoring effects of different indicators show that the method has higher accuracy and retains the ability to dynamically update data.

A time series modeling approach for damage monitoring of concrete dam under seismic effects

In order to improve the applicability of time series models for the diagnosis of concrete dam damage under seismic loading, this paper proposes a diagnostic method for structural damage by combining linear time series modeling and non-linear modeling of model residuals. Starting from the linear structural dynamic response transmissibility function, the expressions of the generalized Auto-Regressive with eXtra inputs (GARX) model for the dynamic response under stationary excitation conditions were derived. The GARX model with dynamic coefficients was extended to model the dynamic response under seismic loading and the generalized Auto-Regressive Conditional Heteroscedasticity (GARCH) model was used to nonlinearly model the model residuals. To track the coefficients of the GARX model, an adaptive least squares recursion method based on fuzzy forgetting factor was studied. The damage indicator of Minkowski distance based on the GARCH model coefficients was proposed. Finally, the effectiveness of the diagnostic methods of the GARX and GARCH models was verified by a numerical calculation of the non-linear damage to a dam. The results showed that GARX can effectively describe the input-output relationship of the dam in the absence of damage. After damage occurs, the GARCH model and the improved Minkowski distance index for the model residuals of GARX can effectively characterize the non-linear damage evolution of the dam.

Contact acoustic nonlinearity and local damage resonance for the detection of kissing bonds in structural adhesive joints

Adhesively bonded joints are susceptible to contamination of surfaces during manufacture and environmental deterioration in real operating conditions. These may cause the generation of so-called “kissing bonds” that can dramatically alter the strength of the joint leading to premature failure. Nonlinear acousto-ultrasonic (AU) techniques have shown great potential for monitoring kissing bonds with piezoelectric sensors permanently installed on the structural joint, thus enabling online and in-situ inspection. This paper investigated the combined contact acoustic nonlinearity (CAN) and local damage resonance (LDR) effects in the presence of kissing bonds in adhesive joints. Experimental nonlinear AU tests showed the formation of LDR frequency down-shifts and “jumps” of the fundamental damage resonance in adhesively bonded aluminium joints, with the kissing bond located internally to the overlapping region between the two adherends. These results were supported by a theoretical model based on the solution of the nonlinear Duffing's equation, under the assumption that the debonded region is a damped nonlinear harmonic oscillator subject to harmonic forcing. The Harmonic Balance Method was used to solve the nonlinear differential problem, showing the generation of frequency down-shifts via the dependence of the ratio between the excitation and LDR frequencies with the amplitude of the fundamental damage resonance. Additionally, two-dimensional finite element simulations using a reduced order model based on the Craig-Bampton technique were carried out to support experimental AU tests for the identification of the LDR frequency and the generation of nonlinear resonance effects. Good agreement between analytical, numerical, and experimental results revealed that a monitoring approach combining CAN and LDR is an extremely efficient and sensitive tool for ensuring integrity and safety of structural adhesive joints.

An approach for fatigue life assessment of a road bridge based on measured corrosion and actual traffic loading

Fatigue and corrosion play a significant role in the aging of steel bridges, especially in a marine environment. An absence of fatigue strength curves for details which are exposed to corrosive environments, realistic traffic load models and accurate damage accumulation models increase the susceptibility of fatigue damage of steel bridges. In this paper, remaining fatigue life of a road bridge is assessed based on the measured corrosion wastage and more realis-tic traffic loads. Corrosion fatigue is also studied as it is one of the main factors that reduce the fatigue life and recently proposed fatigue strength curve for structural details exposed to corrosive environments is utilized for this study. A non-linear fatigue damage accumulation model is used for life assessment apart to the conventional damage model, Miner’s rule. The calculated fatigue lives are compared and discussed in quantitative manner to identify the most conservative remaining life and corresponding methods.

Thermal-fluid-structure coupling progressive failure analysis for the type III composite cylinder under localized fire

Predicting the failure characteristics of composite cylinders under fire is the key to improve the fire resistance and safety of cylinders. However, the current thermal-mechanical coupled failure analysis methods for composite cylinders under fire have several limitations such as oversimplification of the cylinder dome's geometric model and the fire source. To solve these problems, a comprehensive three-dimensional thermal-fluid-structure coupling progressive failure analysis method is developed. This method encompasses a fully coupled conjugate heat transfer model, a FLUENT-ABAQUS data transfer method, and a progressive failure analysis model integrates the Hashin failure criterion and nonlinear damage evolution for fiber reinforced composites. The method is adopted to analyze the fire-resistant performance of a type Ⅲ cylinder to obtain the fire-resistant time, failure pressure and burst location of the cylinder, finding that the pattern of failure pressure depreciation correlates with the burst location of cylinder under localized fire. Besides, the influence of the glass-fiber/epoxy layer on the fire-resistant performance of the cylinder is discussed, demonstrating that even a thin layer of glass-fiber epoxy can significantly increase the fire resistance time of the cylinder.

Sparse polynomial chaos expansion for high-dimensional nonlinear damage mechanics

Finite Element Simulations in solid mechanics are nowadays common practice in engineering. However, considering uncertainties based on this powerful method remains a challenging task, especially when nonlinearities and high stochastic dimensions have to be taken into account. Although Monte Carlo Simulation (MCS) is a robust method, the computational burden is high, especially when a nonlinear finite element analysis has to be performed behind each sample. To overcome this burden, several “model-order reduction” techniques have been discussed in the literature. Often, these studies are limited to quite smooth responses (linear or smooth nonlinear models and moderate stochastic dimensions).This paper presents systematic studies of the promising Sparse Polynomial Chaos Expansion (SPCE) method to investigate the capabilities and limitations of this approach using MCS as a benchmark. A nonlinear damage mechanics problem serves as a reference, which involves random fields of material properties. By this, a clear limitation of SPCE with respect to the stochastic dimensionality could be shown, where, as expected, the advantage over MCS disappears.As part of these investigations, options to optimise SPCE have been studied, such as different error measures and optimisation algorithms. Furthermore, we have found that combining SPCEs with sensitivity analysis to reduce the stochastic dimension improves accuracy in many cases at low computational cost.

A dynamic installation method to improve the morphological characteristics of the bolt-hole contact interface in CFRP interference bolted structures

Dynamic installation (DI) of composite fasteners can reduce interface damage caused by interference and further improve joint performance. Understanding the low-damage mechanisms during DI based on electromagnetic force is critical. In this paper, a 3-D nonlinear progressive damage model based on continuum damage mechanics (CDM) was developed to predict the geometric dimensional variations of the bolt, the damage behavior and stress distribution of the bolt-hole contact interface after interference-fit connection. Static installation (SI) analysis was also considered as a comparative study. Experimental bolt-hole interface damage behavior validated the FEA results. The results show that DI can significantly reduce the installation resistance by thinning and elongating the bolt, so as to remarkably reduce or avoid severe damage to composite laminates, especially for large interference sizes. The low installation damage of the DI specimens results in more uniform residual stresses and higher amplitudes at the hole edges, which may be more conducive to achieving a more uniform stress distribution in the joints under external cyclic loading, thus helping to reduce the incidence of failure and extend the operating horizons of structures.

Estimation and analysis of the cumulative energy damage model for precast concrete nonrectangular column frame structures

A detailed characterization of structural damage progress is essential to performance-based seismic design for precast concrete nonrectangular column (PCNC) frame structures. The paper presents an experimental investigation into the damage behavior of the PCNC frame structures under reverse cyclic loading, including specimens PCFS1 and PCFS2 in bay and specimen PCFS3 in depth of a new precast residential building. Based on the experimental results, the damage mechanism of the PCNC frame structures was further discussed with the cumulative energy damage model proposed in this paper, and the influence of key structural parameters on the damage of the PCNC frame structures was examined, including energy dissipation adjusted factor, the residual deformation rate and the stiffness degradation rate. Available results indicated that the experimental damage curves of test specimens increased with the loading progress and acted with nonlinear damage characteristics, and PCNC frame structural damage behavior was sensitive to the axial compression ratio. For the proposed damage model, the calculation results were in good agreement with the experimental results. On the basis, the damage degree of the PCNC frame structures was divided into five performance levels including normal use, temporary use, use after repair, life safety and prevent collapse in the defined damage range of (0, 1). Elastic layer drift ratio limit was suggested to relax for PCNC frame structures. Final test results could provide a basis for the aseismic design and damage assessment of such structures after earthquake.

Nonlinearity evaluation and damage evolution law of simply supported RC beams based on the FRF similarity measure

Reinforced concrete (RC) beam structures are subject to a certain degree of nonlinearity owing to their material properties and other factors. However, the present evaluation methods for their degree of nonlinearity are only applicable to specific types of excitation. In this study, a nonlinear degree evaluation method suitable for impulse excitation is proposed. The nonlinearity degree (ND) index was defined based on the frequency response function similarity measure, which was used to acquire the structural state and compare multiple states. The effectiveness and noise robustness of the proposed method were verified using numerical examples. Additionally, this method was applied to study the nonlinear damage relationship characteristics of RC beam structures. The normalized value given by the ND index accurately determines the relative nonlinear degree and evolution law of the damage state of simply supported RC beams and further clarifies the nonlinear damage relationship. Finally, the control mechanism of the nonlinear factors was revealed by comparing the nonlinear damage relationships of RC beams with different structural properties. This study provides a simple and effective new method for assessing the degree of nonlinearity in engineering structures and further improves the empirical theoretical system of nonlinear damage relationships for RC beam structures.

Progressive pseudograin damage accumulation model for short fiber-reinforced plastics and its application to fatigue life prediction

A progressive pseudograin damage accumulation (PPDA) model is proposed to predict the fatigue life of short fiber-reinforced plastics (SFRPs), combining viscoelastic-viscoplastic (VEVP) two-step homogenization theory with Chaboche fatigue damage model. Each representative volume element (RVE) of SFRPs is decomposed into pseudograins using a two-step homogenization framework. Then, the fatigue life of each pseudograin is predicted using a master S-N curve, which is prepared based on the “normalized fatigue factor” taking into account both the stress ratio and multiaxial stress state. Thereafter, the overall failure of RVE is predicted by a PPDA model, in which each pseudograin fails progressively considering the stress concentration of the living pseudograins, resulting in non-linear fatigue damage evolution. Finally, the PPDA model is successfully implemented into ABAQUS user material subroutine (UMAT), predicting the fatigue lifetime in good agreement with experimental data.

Study on valley deformation of high arch dams based on nonlinear rheological damage model

The scale of the high arch dam project is large, and the water level is high. The construction and water storage effect will significantly impact the rock mass of the high slopes on both sides, especially on the structural planes such as internal faults. Based on the Jinping Ⅰ high arch dam, an improved Nishihara rheological damage model was established to address the phenomenon of valley shrinkage deformation. The stress and deformation states of the rock mass and dam in the reservoir area were calculated, and the results were compared with the conventional elastic–plastic finite element method. The results indicate that the improved parallel Nishihara rheological damage model can better conform to the deformation properties of the internal structural planes of the rock mass, and the calculation results using this model are closer to the actual deformation situation. When considering the structural plane's rheological characteristics, the valley shrinkage deformation law is consistent with the conventional elastic–plastic finite element calculation results, but the magnitude is too large. In addition, when considering the rheological characteristics of the structural plane, the increase in valley shrinkage deformation value further increases the stress and deformation of the high arch dam, which can better reflect the dam's working behavior and ensure the dam's safe operation.

Shear behaviour of embedded nut-bolted connectors in precast steel-concrete composite beams: Experimental investigations and numerical analyses

Precast steel–concrete composite beam (PSCCB) has been applied extensively in bridge constructions owing to its excellent mechanical properties. Employing demountable embedded nut-bolted connectors (ENBCs) in PSCCBs has become a competitive solution to conveniently replace deteriorated components and to further extend their service life. However, investigations pertaining to shear behaviours of ENBCs in PSCCBs are limited. Hence, economical push-out tests are conducted for investigating the ENBC performance in PSCCBs. Experimental results show that increasing bolt diameters significantly improves the shear performance of ENBCs. Increasing the ring width enhances the initial shear stiffness slightly, minimally affects the ultimate shear capacity, and significantly reduces the slip capacity. Additionally, a finite element model is developed based on the present experimental results to capture the nonlinear response and damage processes of the ENBCs. Subsequently, a validated model is used for parametric studies. Results of numerical analyses show that larger bolt diameters and higher grades improve the shear behaviour of the ENBCs. In addition, steel beams and concrete with lower strengths increase the slip capacity. The pretension degree of the bolts significantly affects the initial shear stiffness of the composite beams. However, the embedded nut angle minimally affects the shear behaviour of the ENBCs. Additionally, the model provided in Eurocode 4 yields slightly conservative predictions for calculating the ultimate shear capacity of ENBCs, thus, a reliable predicted model was proposed for hexagonal-ENBC. Based on experimental analyses, the mechanism associated with the shear and internal stress variations of the ENBCs are revealed via the verified model.

VHXLA: A post-earthquake damage prediction method for high-speed railway track-bridge system using VMD and hybrid neural network

The timely and accurate prediction of post-earthquake damage is critically important for ensuring the safety of high-speed railway track-bridge systems. The study introduces a novel method known as the VHXLA model. This innovative model blends variational mode decomposition (VMD) with a hybrid neural network for predicting non-linear multi-component post-earthquake damage in high-speed railways. The VHXLA model comprises a signal processing module and a deep learning module. The signal processing module utilises VMD decomposition, and the Hilbert transform (HT) to transform two-dimensional seismic signals into four-dimensional complex time–frequency signals, thus simplifying the task of identifying seismic time–frequency characteristics via the neural network. The deep learning module integrates diverse types of neural network components, such as the Xception CNN feature extraction submodule, the LSTM RNN temporal learning submodule, and the multi-head attention mechanism submodule. A Bayesian self-optimisation method is implemented to determine the number of decomposition layers in VMD and select essential hyperparameters. The model's effectiveness is evaluated by predicting the damage of an experimentally validated finite element model, subjecting it to seismic loads, and thus gauging its performance. The results indicated that the signal processing module, based on VMD decomposition, significantly improves the neural network's signal processing capability. In addition, the synergistic integration of different modules in the VHXLA model provides superior prediction accuracy compared to pre-existing damage prediction models. Notably, the prediction accuracy is consistent across different positions of the same predicted component in the high-speed railway track-bridge system.

Damage constitutive model and numerical simulation of in-plane tear failure for architectural fabric membranes

Tearing failure is the key factor affecting the safety of tension fabric structures, but there is a lack of material damage models and numerical methods needed to simulate tearing failure. This paper investigates the macroscopic damage model of architectural fabrics and the numerical simulation method for its tearing failure. Firstly, based on the incremental stress update scheme, theoretical descriptions of the material model considering the nonlinear elastic damage behavior are presented. Then, the influence of stiffness softening laws and the mesh schemes are investigated, and the advantages of easy implantation and good precision of the proposed model are validated by comparison with the cohesive element model embedded in ABAQUS. Compared with the experiment results and theoretical model, the predicted results are in good agreement for various crack length cases, and the nonlinear variation mechanism of tearing residual strength is revealed. Also, the effect of the tensile strength and fracture energy are discussed, and it is found that the crack tip blunting effect causes the linear elastic fracture mechanics not applicable.

High-velocity impact failure modeling of Armox 500T steel: Model validation and application to structural design

As an advanced fracture model, the Generalized Incremental Stress State dependent damage MOdel (GISSMO) provides non-linear damage accumulation formulation to better predict ductile fracture initiation associated with a wider range of material stress states. In this study, we simulate the high-velocity impact failure of Armox 500T steel through computational finite element modeling in the LS-DYNA/Explicit solver. Here, the GISSMO is used to describe the ballistic responses of the Armox 500T steel under dynamic impacts. Two sets of the most important parameters in the GISSMO (i.e., the fracture and instability surfaces) are determined for the Armox 500T steel. The GISSMO is calibrated in terms of the fade exponent and mesh regularization functions using the force–displacement curve of tensile tests extracted from the literature. The calibrated GISSMO is then scaled with the strain rate and validated by comparing quantitative measurements from ballistic experiments provided in the literature. Once validated, the model is then used to investigate the impact failure behaviors of Armox 500T steel by simulating bi-layer configurations consisting of an Armox 500T steel front plate and a rolled homogeneous armor (RHA) steel backing plate impact from a 20 mm fragment simulating projectile. The roles of the standoff distance and impact angle of obliquity on impact failure behaviors of bi-layered steel systems are explored. Altogether, results from this study provide new capabilities and insights into the design of armor structures with respect to lightweight and ballistic performance, and evaluation of impact failure behaviors of Armox 500T/RHA bi-layered systems.

Temperature dependence of the properties of the Li0.81Ag0.19InSe2 nonlinear crystal

The factors that determine the prospects of a crystal for frequency conversion of laser radiation in a wide range to the mid and far infrared (IR) ranges are nonlinear parameters and laser damage threshold (LDT). The latter is determined by the band gap and thermophysical characteristics. This work was devoted to studying the features of the structure change of the Li0.81Ag0.19InSe2 crystal in the temperature range 90–490 K. The temperature dependences of the thermal expansion coefficients, dispersion and optical characteristics in this range were studied. A relationship between the temperature change in the structure and other parameters has been established. In Li0.81Ag0.19InSe2 crystals, pyroluminescence was observed during heating or cooling in the range of 100–300 K, which indicates the crystal is attributed to pyroelectrics. The dispersion characteristics (nx, ny and nz) for wavelengths of 2 and 7 μm were studied, the values of birefringence Δn (nz - nx) were calculated in the temperature range 300–500 K. The detected fluctuations of Δn in the temperature range from 300 to 478 K may be associated with structural changes.