Nonlinear Behavior Research Articles

Enhancing the Range and Reliability of the Spacer Layer Imaging Method

The spacer layer imaging method (SLIM) is widely used to measure the thickness of additive and lubricant films, in lubricant development and evaluation, and for fundamental research into elastohydrodynamic lubrication and tribofilm formation mechanisms. The film thickness measurement, as implemented on several popular tribometers, provides powerful, non-destructive in-situ mapping of film topography with nanometre-scale height sensitivity. However, the results can be highly sensitive to experimental procedure, machine condition, and image analysis, in some cases reporting unphysical film thickness trends. The prevailing image analysis techniques make it challenging to interrogate these errors, often hiding their multivariate nonlinear behaviour from the user by spatial averaging. Herein, several common ‘silent errors’ in the SLIM measurement, including colour matching to incorrect fringe orders, and colour drift due to the optical properties of the system or film itself, are discussed, with examples. A robust suite of novel a priori and a posteriori methods to address these issues, and to improve the accuracy and reliability of the measurement, are also presented, including a novel, computationally inexpensive circle-finding algorithm for automated image processing. In combination, these methods allow reliable mapping of films up to at least 800 nm in thickness, representing a significant milestone for the utility of SLIM applied to elastohydrodynamic contact.Graphical abstract

Simulation and parameterization of nonlinear elastic behavior of cables

AbstractThis work contributes to the simulation, modeling, and characterization of nonlinear elastic bending behavior within the framework of geometrically nonlinear rod models. These models often assume a linear constitutive bending behavior, which is not sufficient for some complex flexible slender structures. In general, nonlinear elastic behavior often coexists with inelastic behavior. In this work, we incorporate the inelastic deformation into the rod model using reference curvatures. We present an algorithmic approach for simulating the nonlinear elastic bending behavior, which is based on the theory of Cosserat rods, where the static equilibrium is calculated by minimizing the linear elastic energy. For this algorithmic approach, in each iteration the static equilibrium is obtained by minimizing the potential energy with locally constant algorithmic bending stiffness values. These constants are updated according to the given nonlinear elastic constitutive law until the state of the rod converges. To determine the nonlinear elastic constitutive bending behavior of the flexible slender structures (such as cables) from the measured values, we formulate an inverse problem. By solving it we aim to determine a curvature-dependent bending stiffness characteristic and the reference curvatures using the given measured values. We first provide examples using virtual bending measurements, followed by the application of bending measurements on real cables. Solving the inverse problem yields physically plausible results.

Numerical Procedure for Solving the Nonlinear Behaviour of a Spherical Absorber

The aim of the paper is to perform numerical simulations for a system of nonlinear differential equations that describe the behaviour of a spherical absorber placed in a support bowl and to describe the applied techniques. The motion of the sphere is constrained to a plane problem. The derived system of equations is numerically solved using the continuation method and the modified secant method. The absorber's response to different harmonic excitation forces is simulated to demonstrate the applicability of these techniques in its analysis. The dependence of the response amplitude on the angular frequency of excitation is presented graphically. The results also include a response stability analysis using the Routh-Hurwitz criteria.

Coherence-controlled chaotic soliton bunch

Controlling the coherence of chaotic soliton bunch holds the promise to explore novel light-matter interactions and manipulate dynamic events such as rogue waves. However, the coherence control of chaotic soliton bunch remains challenging, as there is a lack of dynamic equilibrium mechanism for stochastic soliton interactions. Here, we develop a strategy to effectively control the coherence of chaotic soliton bunch in a laser. We show that by introducing a lumped fourth-order-dispersion (FOD), the soliton oscillating tails can be formed and generate the potential barriers among the chaotic solitons. The repulsive force between neighboring solitons enabled by the potential barriers gives rise to an alleviation of the soliton fusion/annihilation from stochastic interactions, endowing the capability to control the coherence in chaotic soliton bunch. We envision that this result provides a promising test-bed for a variety of dynamical complexity science and brings new insights into the nonlinear behavior of chaotic laser sources.

Unified analytical and design-oriented models for compressive and tensile membrane actions in RC beam-slab structures under internal column loss

Resisting mechanisms including compressive membrane action (CMA) and tensile membrane action (TMA) are critical for RC beam-slab structures against progressive collapse. However, due to the difficulties in considering the nonlinear behaviors and beam-slab interactions, limited analytical studies are currently available to accurately determine the whole resistance evolution path, let alone a simplified design model. This study presents a unified analytical model and a design-oriented simplified model to predict the whole resistance displacement of RC beam-slab substructures under internal column loss. Both equivalent uniformly distributed load (EUDL) and concentrate load (CL) conditions have been considered. In the analytical model, the beam-slab system is discretized into interior beams and multiple slab strips with consideration of their interaction. The compatibility and equilibrium conditions, curvature equations, and constitutive laws of concrete and reinforcement are incorporated to analyze each beam and slab strip. In the design model, a new strategy is proposed to decompose the structural resistance of membrane effect into summation of two components, CMA and TMA resistances, with explicit expressions. Both developed models are validated through experimental and numerical results and good agreements are achieved. Results of the analytical model show that ignoring the beam-slab interactions can lead to underestimation of structural resistance, especially during the transition from the CMA to TMA. The locations of loading points should be carefully selected to make sure 12-point loading system effective. A rule is also suggested to determine proper locations. The simplified design method gives slightly conservative predictions of structural resistance, and its calculation is easy for engineers to use.

Nonlinear vibration of sandwich beams made of FGM faces and FGP core under multiple moving loads using a quasi-3D theory

This study aims to investigate nonlinear dynamic behavior of sandwich beams constituted by functionally graded material (FGM) faces and functionally graded porous (FGP) core under the action of multiple moving loads. The energy equations based on a quasi-3D beam theory considering several functions of shear deformation were established for producing the nonlinear equations of motion used for describing dynamic responses of beams with various boundary conditions. By using the hybrid processes of the Newton-Raphson iteration procedure, the time-integration approach of Newmark-β, and the Gram-Schmidt-Ritz method, the new results of nonlinear analysis were explored and proposed. Several prime parameters such as the porous coefficient, sandwich thickness ratio, power law index and others that significantly affect the dynamic response of the beams were taken into investigations. It can be concluded that beams under one moving load have larger dynamic deflections compared to that under many moving loads. This is because the distance between the moving loads can produce a bending moment against the beam deformation.

Nonlinear dynamic behavior of a bionic quasi-zero stiffness isolation system inspired by cobweb with the amplification effect

Nonlinear dynamic behavior of a bionic quasi-zero stiffness isolation system inspired by cobweb with the amplification effect

Thermodynamic potential and drag force of the impurity-polariton many-body interaction

Investigating the many-body interaction among polaritons is a fundamental goal in comprehending nonlinear behaviors in microcavity semiconductor systems. Hence, the present study focuses on exploring the many-body interaction between excitons and impurities. It was observed that the energy eigenequation governing this system is of sixth-order, rendering it unsolvable. Consequently, a strategy involving the utilization of impurity weight was employed to partition the initial energy eigenequation into two fourth-order equations, a method deemed suitable for lower order approximations. Subsequently, Green’s function was applied to these two fourth-order equations. The analysis of the computed results, encompassing the energy spectrum, polariton density, and thermodynamic potential of the system, reveals that the many-body interaction between excitons and impurities induces the emergence of novel bound states of quasiparticles. Moreover, the inclusion of impurities leads to a decrease in both energy and density of polaritons. Furthermore, the investigation delves into the drag force exerted by impurities on excitons, demonstrating that the drag force escalates in a second-order fashion with impurity velocity and persists even as impurity velocity increases, surpassing the Landau’s equilibrium theory.

Optimising synthetic datasets for machine learning-based prediction of building damage due to tunnelling

Assessment of tunnelling-induced building damage is a complex Soil-Structure Interaction (SSI) probelm, influenced by numerous geometric and material parameters of both the soil and structures, and is characterised by strong non-linear behaviour. Currently, there is a trend towards developing data-driven models using Machine Learning (ML) to capture this complex behaviour. Given the scarcity of real data, which typically comes from specific case studies, many researchers have turned to creating extensive synthetic datasets via sophisticated and validated numerical models like Finite Element Method (FEM). However, the development of these datasets and the training of advanced ML algorithms present significant challenges. poses significant challenges. Reliance solely on parameter domains and ranges derived from case studies can lead to imbalanced data distributions and subsequently poor performance of models in less populated regions. In this paper, we introduce a strategy for designing optimal high-confidence datasets through an iterative procedure. This process begins with a systematic literature review to determine the importance of parameters, their ranges, and dependencies as they pertain to building damage induced by SSI. Starting with several hundred FEM simulations, we generate an initial dataset and assess its quality and impact through Sensitivity Analysis (SA) studies, statistical modelling, and re-sampling in statistically significant regions. This evaluation allows us to refine the model’s input space, seeking scenarios that mitigate output distribution imbalances. The procedure is repeated until the datasets achieve a satisfactory balance for training metamodels, minimising bias effectively. Our findings highlight the success of this approach in identifying an optimal and feasible input space that significantly reduces imbalanced distributions of output features. This approach not only proves effective in our study but also offers a versatile methodology that could be adapted to other disciplines aiming to generate high-quality synthetic datasets.

An anageometric time scale calculus and its some basic applications

Anageometric calculus is a branch of non-Newtonian calculus introduced by M. Grossman and R. Katz in 1967, in which changes in functional values are measured by linear differences but arguments are measured by ratios. The theory of time scales was initiated by S. Hilger in 1988 to unify continuous and discrete analysis. In this article, we introduce anageometric time scale calculus to discuss dynamic equations in which the values of the independent variable show non-linear behaviour. This newly introduced calculus will be more applicable than other calculi in atomic reactors, growth models, etc. We shall discuss some applications of anageometric time scale calculus on the geometric real field R(G) with its optimality and better accuracy.

Mast Design Performance - Influence of the Non-Linear Elastic Behaviour of Carbon Fibres on the Accuracy of Fluid/Structure Interaction Models for Estimating Mast Bending

_ The masts of racing yachts are generally made of carbon fibre reinforced plastics (CFRP) and are subject to two main loads: dock tuning and the forces exerted by the sails. Both result in compression and bending of the mast. The mast design must ensure that for any given sailing configuration, the mast deflection is matched to the sail design to maximise the boat’s performance. Fluid/structure interaction models are generally employed by sail designers who use a stick model for the structural definition of the mast. The elastic properties of the CFRP plies involved in mast lamination are assumed to be constant in this latter model. However, stiffness increases under tension and decreases under compression (up to 30% at failure depending on the fibre type, standard modulus, intermediate modulus, etc) due to some reversible changes in the microstructure of the carbon fibres. As a result, the actual curvature of the mast can be very different from that calculated with the stick model, leading to a significant error in the actual shape of the sail during sailing. In this work, we use a series of three critical loading cases corresponding to those of an IMOCA mast. The influence of the elastic non-linearity of the CFRP plies on the performance of the racing yacht mast is quantified. It is concluded clearly that this elastic non-linear behaviour of carbon fibres is to be accounted for by sails designers to optimise performance. Such an influence is expected to be even more pronounced on spreader masts such as those used for America’s Cup. Keywords Yacht design; IMOCA mast; Carbon fibre composites; Non-linear elasticity

Shape Morphing of Re‐Entrant Honeycomb Metamaterials for Linear Auxetic Behaviors

A re‐entrant honeycomb structure stands out as one of the most prevalent auxetic metamaterials, characterized by its negative Poisson's ratio. While re‐entrant auxetic structures are capable of achieving tunable Poisson's ratios, they tend to vary with the magnitude of applied strain, thereby exhibiting nonlinear auxetic behaviors. This study proposes a novel re‐entrant structure aimed at achieving linear auxetic behavior by mathematically modifying the shape of a re‐entrant cell. To achieve this objective, a sigmoid‐based shape morphing function is introduced to modify the morphology of the hinge connections within the re‐entrant honeycomb cell. The deformation behavior of the shape‐morphed re‐entrant cell is investigated using finite element analysis (FEA), with variations in the morphing parameter. Two FEA models, namely the unconstrained and constrained models, are developed for fundamental analysis of cell deformation and experimental validation, respectively. Compared to the pure re‐entrant honeycomb structure, the proposed shape morphing reduces the relative variation of Poisson's ratio by 70%, while maintaining its magnitude higher than 1.0. This achievement of linear auxetics with a high Poisson's ratio has the potential to broaden the applications of the proposed auxetic structures to various functional components, including sensors with high linear sensitivity and soft actuators with tunable deformation characteristics.

Improved MTPA and MTPV Optimal Criteria Analysis Based on IPMSM Nonlinear Flux-Linkage Model

The use of interior permanent-magnet synchronous machines (IPMSMs) is prevalent in automotive and vehicle traction applications due to their high efficiency over a wide speed range. Given the high-power-density requirements of automotive IPMSMs, it is imperative to consider the effect of nonlinearities, such as saturation and cross-coupling, on the motor model. The aforementioned nonlinearities render conventional linear motor models incapable of accurately describing the operating characteristics of the IPMSM, including the maximum torque per ampere (MTPA) trajectory, the flux-weakening (FW) trajectory, and the maximum torque per volt (MTPV) trajectory. With respect to the linear motor model, the nonlinear flux-linkage model is gradually receiving attention from researchers. This modeling method represents the nonlinear behavior of the motor through the direct establishment of a bidirectional mapping relationship between flux-linkage and current. It is capable of naturally incorporating the effects of magnetic saturation and cross-coupling factors. However, the analysis of the current trajectory optimal criteria based on this model has not yet been reported. In this paper, the optimal criteria for the MTPA and MTPV current trajectories are analyzed based on the nonlinear flux-linkage model of IPMSMs. Firstly, the nonlinear flux-linkage model of the tested IPMSM is established by the experimental calibration method. The mathematical analytical expressions of the MTPA and MTPV optimal criteria are then analyzed by constructing and solving optimal problems with different objectives. Finally, the current command table applicable to actual motor control is constructed by calculating the current command for different operating conditions according to the optimal criteria proposed in this paper. The validity and feasibility of the optimal criteria proposed in this paper are verified through experimental tests on different operating conditions.

Heat extremes linearly shift with global warming, with frequency doubling per decade since 1979

Abstract Heat extremes have been increasing both in frequency and in intensity in most land regions of the world, and this increase has been attributed to human activities. In the last decade, many outstanding and record shattering heat extremes have occurred worldwide, triggering fears of a nonlinear behaviour or an “acceleration” in the development of heat conditions, considering the warming level when the event occurred. Here we show that the evolution of yearly temperature maxima, with return periods above 10 years, consistently shifts with global temperatures and does not significantly depart from this behaviour in recent years or decades when considered globally or at the scale of continents. This result is obtained by using a classical statistical event attribution technique, where the assumption that the distribution of block-maxima extremes linearly shifts with global warming is tested across years and world land regions. However, the pace of frequency change is large, with the probability of heat extremes exponentially rising and nearly doubling every decade since 1979, particularly when considering events with a return period of about 10 to 50 years in 2000. This makes the climate of a decade ago unrepresentative of today’s climate. Our results overall mean that we do not expect events like the recent outstanding extremes to undergo nonlinear changes, despite fast changes. They also show that assumptions underlying attribution techniques used in many recent studies are consistent with recent temperature trends.

Comparative Analysis of Machine Learning Models for Predicting the Mechanical Behavior of Bio-Based Cellular Composite Sandwich Structures

The growing demand for sustainable materials has significantly increased interest in biocomposites, which are made from renewable raw materials and have excellent mechanical properties. The use of machine learning (ML) can improve our understanding of their mechanical behavior while saving costs and time. In this study, the mechanical behavior of innovative biocomposite sandwich structures under quasi-static out-of-plane compression was investigated using ML algorithms to analyze the effects of geometric variations on load-bearing capacities. A comprehensive dataset of experimental mechanical tests focusing on compression loading was employed, evaluating three ML models—generalized regression neural networks (GRNN), extreme learning machine (ELM), and support vector regression (SVR). Performance indicators such as R-squared (R2), mean absolute error (MAE), and root mean square error (RMSE) were used to compare the models. It was shown that the GRNN model with an RMSE of 0.0301, an MAE of 0.0177, and R2 of 0.9999 in the training dataset, and an RMSE of 0.0874, MAE of 0.0489, and R2 of 0.9993 in the testing set had a higher predictive accuracy. In contrast, the ELM model showed moderate performance, while the SVR model had the lowest accuracy with RMSE, MAE, and R2 values of 0.5769, 0.3782, and 0.9700 for training, and RMSE, MAE, and R2 values of 0.5980, 0.3976 and 0.9695 for testing, suggesting that it has limited effectiveness in predicting the mechanical behavior of the biocomposite structures. The nonlinear load-displacement behavior, including critical peaks and fluctuations, was effectively captured by the GRNN model for both the training and test datasets. The progressive improvement in model performance from SVR to ELM to GRNN was illustrated, highlighting the increasing complexity and capability of machine learning models in capturing detailed nonlinear relationships. The superior performance and generalization ability of the GRNN model were confirmed by the Taylor diagram and Williams plot, with the majority of testing samples falling within the applicability domain, indicating strong generalization to new, unseen data. The results demonstrate the potential of using advanced ML models to accurately predict the mechanical behavior of biocomposites, enabling more efficient and cost-effective development and optimization processes in the field of sustainable materials.

The Effect of Nonlinear Sloshing Response of Water on Seismic Behavior of Reinforced Concrete Elevated Water Tanks

In this study, the fluid-structure interactive behavior by using the Westergaard approach and the Smoothed Particle Hydrodynamics (SPH) method of a 1000 m3 reinforced concrete (RC) elevated water tank under different seismic activities i.e., Kocaeli, Van, Kahramanmaraş and Kobe earthquakes was investigated. In the SPH method, the resulting hydrodynamic pressures were applied to the interior of the wall of the structure as an external force which is made as mass additions to the tank walls in Westergaard approach. With the help of software developed, the load carrying system of the elevated water tank was modeled using the MATLAB Partial Differential Equation Toolbox (PDE) software, based on the finite element method, and its verification was made by comparing with ANSYS software model. Dynamic condensation method was used to perform time history analyses for the cited earthquakes. The time-dependent solutions of partial differential equations are solved with the help of ODE45 functions based on Runge-Kutta method, by arranging the equation of motion in state-space format. The cited tank was analyzed linearly under different seismic activities for empty, half-filled (50%) and full-filled (100%) cases and the obtained results were compared with each other. It has been concluded that considering nonlinear behavior of the fluid during the earthquake with the SPH method provided consistency with the real behavior of RC elevated water tanks and gave more realistic results than the traditional Westergaard approach.

Finite Element Analysis and Optimization of the Rotational Stiffness of Semi-Rigid Base Connection under Simultaneous Moment and Tension

The base connection is flexible, not fully pinned/fixed, implying a nonlinear moment–rotation relationship. This deviates from a linear response, where rotation is not directly proportional to the applied moment. Numerical investigations using the commercial software ABAQUS were conducted to analyze the steel base plate connections. The finite element (FE) models were verified against previous experimental results. Moreover, numerical findings of a comprehensive parametric investigation were conducted. The studied connections were examined with different configurations, including variations in the diameter, spacing, and number of the anchor bolts; the thickness of the base plate; and the applied axial force. The current study aims to use numerical results combined with the whale optimization algorithm (WOA) and classical genetic algorithm (GA) to derive a formulation for the moment–rotation (M-θr) relationship. The distinctive aspect of this formulation is that it aims to simulate the nonlinear rotational behavior exhibited by flexible base connections under combined moment and tension loads, while also considering various parameters such as bolt number/diameter and plate thickness. The findings indicate that the WOA is capable of obtaining an optimal equation for accurately simulating the M-Ɵr relationship. This underscores the ability of the WOA to effectively address the complexity of the problem and provide a reliable equation for predicting the rotational behavior of such connections. Consequently, the WOA method can be utilized to calculate the rotational stiffness at H/150, offering valuable support for engineering design processes.

A Non-Linear Successive Approximation Finite State Machine for ADCs with Robust Performance

This work presents the detailed design of a Successive Approximation Analog to Digital Data Converter (SAR ADC) using bulk 180 nm CMOS IC technology. The focus of the study is on replacing the typical Successive Approximation Register array with a Finite State Machine. This converter features a fully differential and bipolar architecture, which leads to the logic SAR nonlinear behavior. A novel digital control logic mitigates the conversion errors through the conditions in the previous logic states. The logic scheme, in combination with a robust continuous comparator, demonstrates tolerance to Process, Voltage, and Temperature variations. The architecture does not include calibration or additional redundancies in post-layout simulations to emphasize the exclusive benefits of the new SAR logic. The proposed SAR ADC achieves a 14.07 effective number of bits with 7.04 fJ/conversion step Walden figure of merit in biomedical applications.

Nonlinear behaviors in back-gate effects of FDSOI MOSFETs at cryogenic temperatures

In this work, we systematically investigate the DC performance of fully depleted silicon-on-insulator (FD-SOI) MOSFETs at both room and cryogenic temperatures as low as 77 K. The influences of back-gate bias on normal and flip-well devices are measured and analyzed. Both types devices display non-linear behaviors when adjusting the back-gate voltage at cryogenic temperatures. Notably, the non-linear effects are more prominent in normal-well devices. The possible reasons are analyzed and verified by technology computer aided design simulation, suggesting that normal-well devices are more susceptible to the formation of depletion regions between the buried oxide layer and the well. This phenomenon disrupts the linearity of the back-gate effect. This research contributes to understanding and characterizing of the back-gate effects in cryogenic environments and holds potential for high-performance computing applications.

Versatile data-adaptive hyperelastic energy functions for soft materials

Applications of soft materials are customarily linked to complex deformation scenarios and material nonlinearities. In the bioengineering field, soft materials typically mimic the low stiffness of biological matter subjected to extreme deformations. Computational frameworks surge as a versatile tool to assist the design of functional applications. The constitutive model lies at the core of such frameworks. In this regard, the customary extreme non-linear behavior of elastomers poses an additional challenge to thoroughly capture the material behavior. Here, data-driven methodologies hold considerable promise for enhancing constitutive modeling when contrasted with phenomenological approaches. In this investigation, we introduce a versatile data-adaptive method tailored to the modeling of hyperelastic soft materials at finite strains. Specifically, our method substitutes an a priori chosen model for the strain energy function by a flexible interpolant defined on a discretized invariant space. Within this framework, the interpolation values assume the role of material parameters and are determined through finite element model updating to conform to measured experimental data — comprising full-field displacements coming from Digital-Image-Correlation and global reaction forces. We validate the method on uniaxial experimental tests of soft elastomers, encompassing ELASTOSILTM, DOWSILTM, and V HBTM. Overall, we aim to establish a new route for the construction of hyperelastic energy functions, untethered from any predefined existing models or assumptions regarding the shape of the energy.