Nonlinear Behavior Research Articles

Elucidating Nonlinear Stress Relaxation in Transient Networks through Two-Dimensional Rheo-Optics.

This study aims to elucidate the origin of nonlinear stress relaxation behaviors in transient networks using a systematically controlled model system consisting of the tetra-armed polyethylene glycols (Tetra-PEG slime) in conjunction with two-dimensional rheo-optics observations. Transient networks, characterized by their temporary cross-links, are extensively utilized in self-healing and robust materials. However, the molecular mechanisms governing their viscoelastic responses to large deformations have remained elusive. This is primarily due to the heterogeneous structures inherent in conventional transient networks and a scarcity of detailed experimental evaluations. By employing Tetra-PEG slime, which is distinguished by its regular structure with uniform strand lengths and functionalities, and the polarization imaging method, we overcome these obstacles. Our results reveal that the damping phenomena observed under large step strains arise from spatially heterogeneous relaxation, predominantly driven by network strand pullout. These insights lay a solid foundation for understanding the intricate rheological properties of transient networks.

New OpenSees material model for simulating reinforced concrete shear walls subjected to coupled axial tension and cyclic lateral loads

In high-rise buildings, reinforced concrete (RC) shear walls, particularly those forming part of coupled wall systems or core wall systems, may be subjected to coupled axial tension and cyclic lateral loads during strong seismic events. A new two-dimensional material model named the “Fixed Angle Model Considering Crack Sliding” (FAM-CS) was proposed for simulating the nonlinear behavior of RC walls subjected to axial tension and cyclic lateral loads. The proposed model was implemented in the OpenSees platform. Nonlinear constitutive models for shear aggregate interlock effects of concrete and dowel action of rebars were incorporated into the proposed model to represent the shear transfer mechanisms along concrete cracks. The proposed model was validated against the test data of six wall specimens subjected to coupled axial tension and cyclic lateral loads. The results indicated that the proposed model reasonably predicted the lateral strength capacity (an average error of 6.2 %) and the residual strength at the maximum drift loading (an average error of 12.3 %) of the specimens. For comparison, three other commonly used models, the Shear-Flexure Interaction Multiple-Vertical-Line-Element-Model, the multi-layer shell element model and the Cyclic Softened Membrane Model were adopted for the simulation of the specimens. Compared with the three existing OpenSees models, the newly implemented material model provided improved predictions of the wall hysteretic behavior with respect to lateral strength capacity, lateral strength degradation, pinching characteristics and cyclic stiffness degradation. In addition, the proposed model reasonably captured the localized failure pattern as well as the energy dissipation characteristics of the test specimens. Finally, a mesh sensitivity study was conducted to assess the robustness of the proposed model. The results revealed that the proposed model was robust regarding the lateral load-drift responses of RC walls, with a mesh size ranging from approximately one to three times the average crack spacing.

High-frequency nonlinear vibration analysis through low-frequency stereo-camera systems

This paper describes a new methodology that expands the capabilities of low-frame, high-resolution stereo-camera systems in studying the dynamic behavior of components in the presence of nonlinear phenomena. A new downsampling technique called the Smoothed Harmonics Analysis (SHA) is proposed. This technique addresses the limitations due to the low-frame rate cameras for the study of high-frequency periodic steady-state nonlinear oscillations. SHA enables accurate reconstruction of downsampled signals, thus opening up numerous potential applications. The feasibility of this technique is demonstrated by analyzing the motion of a beam with nonlinear behavior. The nonlinearity is caused by intermittent contact while the beam is subjected to harmonic excitation.

Mechanical characterisation and high temperature analysis of hyperelastic adhesives – Modelling and experimental validation

Adhesive bonds are subject to multiple environmental conditions that can affect their mechanical performance during service. Therefore, it is important to evaluate the influence of temperature on adhesive strength, as it can impact joint safety and should be considered during the design phase. This study presents an analysis of the effect of high temperatures on the mechanical behaviour of joints made with highly elastic adhesives, specifically a polyurethane and a silicon-modified polymer. Shear and tensile tests were conducted at temperatures of 23, 50, and 80 °C using dumbbell specimens for tensile tests and single lap specimens (SLJ) for shear tests. The tests were performed with two different substrates, aluminium (Al) and glass fibre reinforced polyester panel (GRP), and with varying adhesive thicknesses. These tests aim to assess the impact of temperature conditions on the mechanical properties of the adhesive and the behaviour of the joints. The analysis of the experimental results reveals that the adhesive degrades when exposed to high temperatures, resulting in reduced strength and stiffness, and less linear behaviour.Furthermore, this work involves the determination of a model able to reproduce the mechanical behaviour of hyperelastic adhesive at high temperatures, considering diverse constitutive modelling approaches. To achieve this, a testing protocol was conducted on basic uniaxial and planar specimens. The results indicate that the Ogden N=2 model is the most suitable for representing the non-linear behaviour of the hyperelastic adhesive at high temperatures. In contrast, the Mooney Rivlin model is more suitable to represent the material behaviour under ambient conditions. To conclude this work, the law has been satisfactorily validated by comparing the results of tests carried out on SLJ specimens with different adhesive thicknesses.

Control of a building system with sudden nonlinearity using the sliding mode technique

In civil engineering application such as the seismic resistant structural design, a building system often enters into its nonlinear range to minimize the force transfer to the superstructure. An ideal control design should enhance the usefulness of the nonlinear behavior by diminishing its adverse effects at a minimal control input. This study developed a unified feedback mechanism based on the sliding mode control approach that fostered the multiple selected modal control of a structural system undergoing linear and nonlinear stages of hysteretic deformations. The ideal sliding surface for controlling a specific mode was designed based on the interaction characteristics between two modes at two different stages of deformation. An ′ S′ type functional form of the control force was developed on either side of the sliding surface based on the velocity feedback of the system by ensuring reachability to the ideal sliding surface. To demonstrate the effectiveness of the adopted control, a five-story shear building with uniform mass and initial stiffness distribution with concentrated nonlinearity at the base column was considered under 10 earthquake excitations. The system was studied under the proposed control along with the uncontrolled system. In addition to the adopted control, a popular and existing LQG control technique was also implemented based on the equivalent linearized structural system for comparison. The adopted control provided the desired performance of the structural system while keeping the effectiveness of the system’s nonlinearity under earthquake excitations. Considering the system’s responses and the input control force, the efficiency of the adopted mechanism outperformed the LQG control, which was found to amplify the unfavorable effects of the system’s nonlinearity.

Simulation of soil-structure interaction using inelasticity-separated finite element method

The soil–structure interaction (SSI) effect is nonnegligible during the nonlinear seismic response analysis of large-scale or underground structures. However, the computation of nonlinear response of a structure considering SSI effect usually is a time-consuming process because the numerical model should involve the structure itself, a wide-range soil domain and the soil–structure interface, especially for large-scale structure. This study aims to incorporate the inelasticity-separated finite element method (IS-FEM), which is an algorithm recently developed for efficient structural nonlinear analysis, to improve the efficiency of the soil-structure interaction system. To this end, an inelasticity-separated contact element model for modeling the nonlinear behavior of soil and structure interface is developed in this study. To derive the inelasticity-separated governing equation of this model, a reference elastic stiffness is defined so that the normal and shear deformation of any point pair in the presented contact element is decomposed into reference linear and reference nonlinear parts according to this reference elastic stiffness. As a result, the problem of inconsistency between the requirement of IS-FEM for constant initial linear elastic stiffness and the existence of inflection point for the stress versus relative displacement relationship of contact behavior can be solved. Then, the Goodman element formulation for depicting the nonlinear contact behavior is introduced and an interpolation scheme to establish the reference nonlinear deformation field in an element is incorporated. By combining the proposed model with existing inelasticity-separated elements, a global analytical model of the soil–structure interaction system can be established within the framework of IS-FEM. Because the nonlinearity usually occur in some local regions of the global model and the use of the IS-FEM only require performing these operations for a small scale matrix representing local nonlinearity, the computational efficiency of nonlinear structural response analysis considering SSI effect can be improved significantly. The applicability and efficiency of the proposed method is finally verified by two numerical examples.

Impact of environmental stochastic fluctuations on the evolutionary stability of imitation dynamics.

To show the impact of environmental noise on imitation dynamics, the stochastic stability and stochastic evolutionary stability of a discrete-time imitation dynamics with random payoffs are studied in this paper. Based on the stochastic local stability of fixation states and constant interior equilibria in a two-phenotype model, we extend the concept of stochastic evolutionary stability to the stochastic imitation dynamics, which is defined as a strategy such that, if all the members of the population adopt it, then the probability for any mutant strategy to invade the population successfully under the influence of natural selection is arbitrarily low. Our main results show clearly that the stochastic evolutionary stability of the system depends only on the properties of the mean matrix of the random payoff matrix and is independent of the randomness of the random payoff matrix. Moreover, as two examples, we show also that under the framework of stochastic imitation dynamics, the noise intensity affects the evolution of cooperative behavior in a stochastic prisoner's dilemma game and the system's nonlinear dynamic behavior.

Nonlinear finite element damage analysis of laminated shells by Carrera Unified Formulation

The paper presents a comprehensive study on the nonlinear finite element analysis of laminated shells, employing the Carrera Unified Formulation (CUF) in conjunction with a progressive damage model developed by Tita et al. (2008). This research focuses on accurately predicting the behavior of laminated composite structures under progressive damage. The model accounts for both polymer matrix and fiber failures, and the numerical implementation and simulations are performed using MATLAB. The study validates the proposed framework by comparing the numerical results with experimental data, demonstrating a good agreement and thus confirming the model’s capability to capture the nonlinear behavior of laminated shells during damage progression. The research also highlights the importance of the CUF in providing a versatile approach to finite element analysis, allowing for different families of elements and, thickness expansions and use of failure criteria that consider out of plane stresses, which can be particularly useful for a more detailed and physically consistent analysis of damage in composite materials.

The nonlinear rainfall–quick flow relationships in a humid mountainous area: Roles of soil thickness and forest type

The nonlinear behavior of hillslope quick flow (QF) in response to variations in soil thickness and forest types remains unclear due to uncertainties or unknown features in field studies, hindering accurate interpretation of their impact on QF. To this end, three artificial physical models with different mineral soil thickness (0 cm, shallow 50 cm, and thick 150 cm) beneath a 50 cm root zone for each forest (i.e., the broadleaf and coniferous forests) were constructed and intensively monitored. Results showed that the threshold-based QF was a function of the sum of rainfall amount and antecedent soil wetness, which was isolated by two breakpoints—the generation and rising thresholds—across all artificial physical models. These breakpoints indicated the storage thresholds for QF generation and the transition from slow to fast QF in humid forests. The broadleaf forest required more rainfall to reach the generation threshold due to higher litter interception capacity and soil water deficit by plant water uptake compared to the coniferous forest. Above the rising threshold phase, QF increased rapidly and linearly due to the establishment of flow path connectivity driven by soil water content, with the broadleaf forest showing a faster increase in QF than the coniferous forest. The dominant preferential/unsaturated flow in humid mountainous areas was also confirmed. Preferential flow paths were well-connected in the root zone and extended to the shallow mineral soil, resulting in an insignificant difference in mean QF between forest types. The thick mineral soil disrupted preferential flow path connectivity, leading to a greater amount of water being laterally diverted and retained within the soil. Consequently, a sharp decrease in QF was observed in hillslope with the root zone capping thick mineral soil for both forests. Our results highlighted the application of threshold-based theory and controlled experiments in enhancing the comprehension of the fundamental physical mechanism governing runoff processes in humid forests.

Nonlinear flow phenomenon of a power-law non-Newtonian fluid falling down a cylinder surface

In this paper, we present a comprehensive study of the fingering phenomenon of a power-law non-Newtonian fluid falling down a cylinder surface. A theoretical analysis is firstly carried out and the governing equation describing the film thickness is established for the non-Newtonian fluid denoted by a power-law index n. Using the lubrication theory with dimensionless variables, the partial differential equation for the film thickness is derived, and both two-dimensional flow and three-dimensional flow are investigated. The traveling wave characteristic of the two-dimensional flow is displayed by using the finite difference scheme associated with a Newton iteration technique. The effect of changing the radius of the cylinder, precursor-layer thickness and power-law index is then considered through examining the variation of the capillary waves. Furthermore in three-dimensional complex flow, the fingering patterns for different parameters are simulated. The linear stability analysis based on the traveling wave solutions is given to elucidate the influence of different physical parameters, explaining the physical mechanism of nonlinear flow behaviors in two dimension and three dimension. Results from linear stability analysis show that the power-law index reinforces the fingering instability whether the fluid is shear-thinning or shear-thickening. Moreover, the numerical results illustrate that increasing the radii of the cylinder expands the unstable region. The flow profiles for different power-law coefficients are consistent with the result of the linear stability analysis, proving the unstable role of the power-law coefficient.

Nonlinear dynamic response of a sandwich plate with negative Poisson’s ratio honeycomb-core layer under low-velocity collision impact

In this paper, a nonlinear analytical model is presented for the low-velocity collision impact of a sandwich plate with auxetic honeycomb-core layer. The auxetic feature of the honeycomb material is realized by mathematically expressing the effective material coefficients in terms of material property and cellular geometric parameters through a homogenization method. The higher order shear deformation theory, the von Kármán nonlinearity theory, and a modified Hertz contact law which accounts for the contact pressure distribution and indentation effect, are employed to establish the kinematic relations. The Newmark time integration scheme in conjunction with the direct iterative method is utilized to establish a solution procedure for the nonlinear dynamic governing equation. The verification of the presented model with the data in published literatures is carried out, followed by a series of numerical analyses for influences of cellular geometric features and impactor’s initial conditions (such as impactor’s initial velocity, mass, and nose curvature radius) on the nonlinear dynamic response. The results of numerical analyses show that the geometric features of the unit cell in the honeycomb-core and impactor’s initial conditions can cause significant influences on the nonlinear collision impact behaviors of the system.

Analysis, design, and optimization based on genetic algorithms of a highly efficient dual-band rectenna system for radiofrequency energy-harvesting applications

This paper gives an enhanced Rectenna design that operates at dual-band [2.45 and 5.8] GHz in the ISM (Industrial, Scientific, and Medical) band and is printed on an FR4-Epoxy substrate. This Rectenna design includes two proposed sub-designs for the receiving antenna and rectifier circuit based on the microstrip technology. The first sub-design concerns the microstrip patch antenna (MPA) described by its radiating element as a pentagonal, its ground being affected by a defective ground structure technique, and its polarization manner as circular polarization. This MPA design is analyzed, designed, optimized using genetic algorithms (GAs), simulated under CST MWS (i.e., computer simulation technology microwave studio), and confirmed by another software named HFSS (high-frequency structure simulator). The second sub-design concerns the microstrip rectifier circuit (MRC) that contains an input matching network based on a coupled-line impedance transformer strategy to achieve good adaptation between MPA and MRC, voltage doubler converter using an SMS7630 Schottky diode thanks to its high sensitivity, microstrip interdigital capacitor to mitigate the intrinsic losses due to the lumped elements, harmonic rejection filter based on a stepped-impedance low-pass filter to reject the unwanted harmonics generated by the non-linear behavior of SMS7630, and the resistive load that models the consumption of the system to be fed. This MRC is analyzed, designed, optimized using GAs, and simulated under ADS (Advanced Design System). The effectiveness of the proposed MPA is proven in terms of gain equals 3.06 dBi and 4.683 dBi at 2.45 GHz and 5.8 GHz respectively, and efficiency equals 95.13 % and 96.552 % at 2.45 GHz and 5.8 GHz respectively. The proposed MRC is effective in terms of efficiency at a lower input power value of about 97.18 % and 67.93 % at 2.45 GHz and 5.8 GHz respectively.

Combined effect of track-bridge interaction on the dynamic response of a simply supported railway bridge

In this work, the objective is to understand the effect of the nonlinear behaviour of the ballasted track, or the mechanism of vertical and horizontal track-bridge interaction behaviour, on the dynamic response of a simply supported railway bridge, carrying a single ballasted track characterized by a fractional order viscoelastic nonlinear Winkler foundation type, and acted by a moving train load with constant speed. The main feature of the model is that the horizontal and vertical interactions at the interface between the bridge deck and the ballasted track, composed by rails, sleepers and ballast, is introduced through a nonlinear cubic force-displacement relation, schematizing the nonlinear stiffness, plus fractional derivative term for simulating the rail bed’s damping behaviour and a system of horizontally orientated spring-damper elements. By applying the two numerical methods, fourth-order Runge-Kutta method and Finite Difference Method, the validation of the dynamic behaviour of the rail-bridge system is performed, and numerical simulations demonstrate the accuracy of the proposed theoretical model for predicting the real behaviour of the studied bridge taking into account the track-bridge interaction effect. The influence of the fractional-order derivative and the distance between sleepers on the critical velocities, associated with resonance effects, is also addressed.

On the Nonlinear Behavior of Composite Structures under Multiple Earthquakes Considering Soil–Structure Interaction

On the Nonlinear Behavior of Composite Structures under Multiple Earthquakes Considering Soil–Structure Interaction

Clutching inertial system for base-isolated liquid storage tanks: Seismic performance and optimal parameters

Liquid storage tanks (LSTs) are susceptible to significant damage during earthquake events, necessitating their continued functionality and additional protection through isolation techniques. The sloshing response and overall base shear of LSTs are critical factors, particularly in base isolated (BI) tanks. This study aims to enhance the seismic resilience of LSTs by leveraging a newly developed advanced inerter-based vibration control methodology for structures. This innovative approach integrates a supplemental clutching inertial system (CIS) with a laminated rubber isolator (LRB). Utilizing an equivalent linearization technique, the study evaluates the equivalent damping and inertance constants to account for the nonlinear behavior of the CIS. These equivalent parameters are then used to assess the stationary peak response of the isolated tank structure, which encompasses sloshing and bearing displacements, forces within the CIS and the isolator, and the total base shear. Further, the analysis employs the stationary power spectral density function (PSDF) model of earthquake excitation by Kanai-Tajimi and the performance of the inerter-based hybrid control strategy is examined by varying system parameters, such as isolation period, isolation damping, CIS inertance mass ratio, and the tank's aspect ratio (i.e., broad or slender). An optimal inertance of the CIS is identified, leading to the least overall base shear for both isolated tank configurations. The impact of these parameters inertance mass ratio of the CIS is also investigated. Subsequently, the isolated tanks are exposed to eleven near-fault (NF) and far-field (FF) real-time earthquake excitations. The study evaluates the CIS's performance as an auxiliary system during these seismic events and contrasts the outcomes with the seismic response under stochastic excitations. The results highlight the effectiveness of the advanced inerter-based hybrid control strategy in reducing the seismic response of isolated tank configurations.

On Quantification of the Nonlinearity of PPV in Model Evaluation with Imbalanced Datasets

This paper presents a quantitative analysis of the nonlinearities of the positive predictive value (PPV) and its effect in evaluating two-class pattern classification models with imbalanced datasets. The analysis is made through an expression of the PPV as a function of two other classification ratios that are invariant to the data imbalance —the true positive rate (TPR) and false positive rate (FPR), and [Formula: see text] — the imbalance ratio (IR) of the dataset such that PPV [Formula: see text]TPR/([Formula: see text]TPR[Formula: see text]FPR). The curvatures of PPV in the three-dimensional TPR–FPR–[Formula: see text] space are studied using the Hessian matrix, from which a saddle-shaped 3D surface in the space is revealed. This paper explores the nonlinear behaviors of PPV around the critical points, identified at FPR [Formula: see text]TPR on the saddle surface, along with its scaling and sensitivity issues as performance measurements in model evaluation. The effect of the nonlinearities of PPV for the F1 and MCC metrics on imbalanced datasets is also studied. It is warned through the results of this study that the evaluations of classification models could be misleading if without an awareness and understanding of the nonlinearities associated with the PPV and its relevant metrics on imbalanced datasets.

Nonlinear dynamic study of FG-GFRC-NPR structures

The functionally graded glass fibre-reinforced polymer composite(FG-GFRC) is one of the contemporary sophisticated materials that may be employed for a variety of technical purposes. The shock absorption capacity of FG-GFRP laminates can be improved by incorporating auxetic property (i.e., negative Poisson's ratio NPR) in the structures, which can be attained by a particular stacking sequence of glass fibres (GF) and a different percentage of GF distribution along the thickness direction within the FG-GFRP structure. The nonlinear dynamic behaviour of such structures must be investigated. The clamped-clamped FG-GFRP-NPR structure is stimulated under a uniform transverse load distribution in the current work. Based on the higher-order shear deformation theory (SDT), the displacement field and nonlinear stress–strain relationship are derived. The nonlinear differential equation with cubic non-linear components were derived using Hamilton’s principle and transformed using Galerkin’s technique and obtained governing equation of motion. MATLAB has been used to conduct all numerical simulations. A time series, a phase picture and a Poincare diagram (PCM) were generated to characterize the vibration behavior of such auxetic structures.

Nonlinear thermo-mechanical static stability analysis of FG-TPMS shallow spherical shells

An analytical solution for the nonlinear static stability problem of functionally graded triply periodic minimal surface (FG-TPMS) shallow spherical shells is studied in the current research for the first time. Three common TPMS structures including Primitive (P), Gyroid (G), and I-graph and Wrapped Package-graph (IWP) with three models of functionally graded porosity distribution along the thickness are considered. The shallow spherical shells (shallow SSs) are subjected to combined thermo-mechanical loadings and rested on a nonlinear elastic foundation. The fundamental formulas are expressed based on the higher-order shear deformation theory (HSDT) and von Kármán's geometrical nonlinearities. Employing the Ritz energy minimization method, the explicit relationship between load and deflection is derived. Subsequently, the static stability behavior of FG-TPMS shallow SSs is investigated. Numerical illustrations are investigated to show the superior thermo-mechanical load-carrying performance of the FG-TPMS SSs compared to corresponding isotropic structures of the same weight. The significant effects of geometric parameters, nonlinear elastic foundation parameters, and the type of FG-TPMS structures on the nonlinear static stability behavior of shallow SSs are further considered.

Parameter Calibration and Verification of Elastoplastic Wet Sand Based on Attention-Retention Fusion Deep Learning Mechanism

The discrete element method (DEM) is a vital numerical approach for analyzing the mechanical behavior of elastoplastic wet sand. However, parameter uncertainty persists within the mapping between constitutive relationships and inherent model parameters. We propose a Parameter calibration neural network based on Attention, Retention, and improved Transformer for Sequential data (PartsNet), which effectively captures the nonlinear mechanical behavior of wet sand and obtains the optimal parameter combination for the Edinburgh elasto-plastic adhesion constitutive model. Variational autoencoder-based principal component ordering is employed by PartsNet to reduce the high-dimensional dynamic response and extract critical parameters along with their weights. Gated recurrent units are combined with a novel sparse multi-head attention mechanism to process sequential data. The fusion information is delivered by residual multilayer perceptron, achieving the association between sequential response and model parameters. The errors in response data generated by calibrated parameters are quantified by PartsNet based on adaptive differentiation and Taylor expansion. Remarkable calibration capabilities are exhibited by PartsNet across six evaluation indicators, surpassing seven other deep learning approaches in the ablation test. The calibration accuracy of PartsNet reaches 91.29%, and MSE loss converges to 0.000934. The validation experiments and regression analysis confirmed the generalization capability of PartsNet in the calibration of wet sand. The improved sparse attention mechanism optimizes multi-head attention, resulting in a convergence speed of 21.25%. PartsNet contributes to modeling and simulating the precise mechanical properties of complex elastoplastic systems and offers valuable insights for diverse engineering applications.

Real-Time Massive Parallel Generation of Physical Random Bits Using Weak-Resonant-Cavity Fabry-Perot Laser Diodes

We experimentally demonstrate a scheme for generating massively parallel and real-time physical random bits (PRBs) by using weak-resonant-cavity Fabry-Perot laser diodes (WRC-FPLDs) with optical feedback. By using external optical feedback to modify the nonlinear dynamic behavior of the longitudinal modes in WRC-FPLDs, the chaotic behavior of each channel can be induced under suitable feedback strength. By filtering these longitudinal modes, a real-time PRBs at 10 Gbits/s can be generated by using field programmable gate array (FPGA) board for the real-time post-processing of a single-channel chaotic signal. Considering the presence of up to 70 longitudinal modes within a broad spectral range exceeding 40 nm, each of these modes can be used to extract chaotic time sequences for random number generation. Therefore, our PRB generation scheme has the potential to achieve a data throughput of over 700 Gbits/s.