Nonlinear Range Research Articles

Nonlinear Relaxation Time in Glassy Poly(methyl methacrylate) Subjected to Tensile Creep Stresses

Nonlinear viscoelastic behavior of glassy poly(methyl methacrylate) (PMMA) subjected to high tensile creep stresses was studied. Right after the loading of creep stress, a rapid decrease of strain rate as a function of strain was observed, indicating behavior of linear viscoelastic solid. Then after showing a sharp minimum, the strain rate gradually increased due to nonlinear flow and reached to almost constant maximum values at steady flow state, and then slightly decreased. Strain range in which the nonlinear flow was observed did not strongly depend on the magnitude of creep stress and temperature, although magnitude of strain rate was obviously affected by these conditions. Nonlinear single relaxation time τ for the glass in the nonlinear flow range of strain was evaluated by means of a simple mechanical model. The nonlinear relaxation time τ decreased with increasing time t to a steady value appeared in the steady flow state. A quantity τ/t was found to be an almost unique decreasing function of strain independently of differences in magnitude of creep stress and temperature. This characteristic dependence of relaxation time τ on strain was considered as a result of a constant decreasing slope of τ-t relation, which slightly depends on the magnitude of stress, during transient flow state under constant high stresses.

Fusion of two stable elastic structures resulting in an unstable system

It is shown that a compound elastic structure, which displays a dynamic instability, may be designed as the union (or ‘fusion’) of two structures which are stable when separately analysed. The compound elastic structure has two degrees of freedom and is made up of a rigid rod connected with two springs to a smooth support, which evidences a jump in the curvature at the equilibrium configuration. Instability is proven in a linearized context and is related to the application of a non-conservative load of the follower type so that the instability disappears under dead loads. In the fully nonlinear range, the instability is also confirmed through numerical simulations. The obtained results may be useful in the design of new mechanical sensors, devices for energy harvesting, or architected materials. In addition, our findings have conceptual implications on piecewise-linear theories of mechanics such as for instance plasticity or frictional contact.

Seismic Assessment of Steel Frames Subjected to Multi-hazards

This paper investigates the effects induced by thunderstorm downbursts to steel building structures that have been previously damaged during strong directivity ground motion events. To achieve this objective, one four-story steel moment-resisting frame that was tested at the E-defense laboratory, Japan was analyzed in the nonlinear range using OpenSees. The seismic response was numerically simulated, obtaining a satisfactory agreement with the experimental evidence, revealing that the effects of such wind events and vertical ground motions were significant. These effects should be addressed during the design of low and medium buildings subjected to initial damage and subsequent thunderstorm downbursts and the ductility demands on structures subjected to multi-hazards can be quantified. The wind loads are applied as an externally applied dynamic load and the revised ductility demands are determined directly. The obtained results are compared to what is expected by experimental tests.

Effects of thermal instability on density limit disruption in J-TEXT

As an important precursor of density limit disruption, thermal instability under J-TEXT high-density discharges is studied in this paper. An extended MHD code called NIMROD [Sovinec et al., J. Comput. Phys. 195, 355 (2004)] is used to explore the intrinsic relationship between density limit disruption and thermal instability. The experimental and simulation results show that radiation from the boundary impurity can cause thermal instability and impurity radiation increases rapidly when the plasma temperature decreases to the nonlinear range of carbon cooling rates, which cools down the plasma and enhances impurity radiation. Further investigations show that the local reduction in thermal instability at the plasma edge shrinks the local current channel and increases the internal current density gradient, which triggers the 2/1 mode and destabilizes the 3/1 and other higher-order modes. Finally, a rapid increase in the MHD instability can cause density limit disruption.

Blast enhanced façade design by means of an optimal balance between security and sustainability

The major objective of this paper is to show that glazed curtain wall has a surprising potential for blast enhancement. However, often this potential is partially lost because of inaccurate and only presumed safe side approach. Indeed, in curtain wall it is much important to assess properly the beneficial effect of the deformable supports, framing and possibly brackets, on the glazing response under blast wave effects. Only in this way a true balanced design approach can be carried out and the protective requirement can be integrated into the façade design by preserving the architectural requirements, comfort, classical energy efficiency requirements and novel demand for sustainability. On the other side the large variability of materials and component behaviour under nonlinear range and the uncertainties related to the blast threat recommend a flexible calculation tool, which must be coupled with a sensitivity analysis on the most relevant inputs. For this reason, a Multi Degree of Freedom approach shows several advantages with respect to the Explicit Dynamic Finite Element Analysis, considering also the large number of geometry, component design and blast load variations are existing in a typical application of the protection on a high rise building. The impact of the calculation method is demonstrated by means of a comparative exercise and by means of real case applications.

Power output estimation of a two-body hinged raft wave energy converter using HF radar measured representative sea states at Wave Hub in the UK

For the physical model testing of wave energy converters (WECs) in the wave basin, it is necessary to test the models in a small number of sea states. Previously, the H – T binning method was widely used to determine the sea states that are representative of an ocean area. However, it omitted much useful information such as the wave directionality. In this paper, a novel method, the K-means clustering technique is used in combination with High Frequency (HF) radar measured data from Wave Hub, UK. The results show that K-means clustering method better preserves the characteristics of the ocean area than the binning method. Furthermore, the impact of different regrouping methods on assessing the annual energy output of the model is investigated, by applying the K-means clustering method to a 1:25 two-body hinged raft WEC. It is found that although non-linear performance can be clearly observed in the model both physically and numerically. Due to the fact that most sea states from Wave Hub are out of the non-linearity range of the model, the non-linear effect on the overall performance of the WEC model in this ocean area is limited. It allows the annual energy output to be accurately predicted by using only a small number of representative sea states (defined as K) ≤15, based on K-means clustering method.

Measuring the linear viscoelastic regime of MCF-7 cells with a monolayer rheometer in the presence of microtubule-active anti-cancer drugs at high concentrations.

The rheological properties of cells have vital functional implications. Depending, for instance, on the life cycle, cells show large cell-to-cell variations making it cumbersome to quantify average viscoelastic properties of cells by single-cell techniques. Microfluidic devices, typically working in the nonlinear viscoelastic range, allow fast analysis of single-cell deformation. Averaging over a large number of cells can also be achieved by studying them in a monolayer between rheometer discs. This technique allows applying well-established rheological standard procedures to cell rheology. It offers further advantages like studying cells in the linear viscoelastic range while quantifying cell vitality. Here, we study the applicability of the technique to rather adverse conditions, like for microtubule-active anti-cancer drugs and for a cell line with large size variation. We found a strong impact of the gap width and of normal forces on the moduli and obtained high vitality levels during the rheological study. To enable studying the impact of microtubule-active drugs on vital cells at concentrations several orders of magnitude beyond the half maximal effective concentration for cytotoxicity, we arrested the cell cycle with hydroxyurea. Irrespective of the high concentrations, we observed no clear impact of the microtubule-active drugs.

Editorial: theme issue on complex rheology in biological systems

Editorial: theme issue on complex rheology in biological systems

Micropolar beam-like structures under large deformation

Results from experimental torsion and bending tests show the existence of a size effect, which conventional continuum models are unable to describe. Therefore, the incorporation of the micropolar media into numerical approaches for the analysis of materials with a complex microstructure looks necessary. So far, most studies utilize Cosserat continuum theory with 3D finite solid elements, even though, it covers only few beam elements developed within a linear strain–displacement relationship, and therefore only works in a small deformation regime. In this study, the authors aim to develop a size-dependent 3D continuum beam element based on the absolute nodal coordinate formulation (ANCF) with microstructure inclusions. Comparing analytical solutions within the Cosserat continuum model and models based on the proposed and already existing 3D micropolar solid elements, one can see a good correlation between them, with a faster convergence rate for the developed ANCF beam element. That allows exploiting the developed beam element within the non-linear deformation range, which is usually bypassed because of high computational costs, thus, accounting fully for differences between two media descriptions.

A modified applied element model for the simulation of plain concrete behaviour

A modified applied element model to simulate the behaviour of plain concrete continuum structures including discrete cracking is proposed in this study. In the classical applied element model, Poisson effects are fully ignored. To remediate this issue, diagonal elements are introduced to include the Poisson effect, and the constitutive parameters are rigorously determined using the Cauchy–Born rule and the hyper-elastic theory. The formulation is validated for linear elastic problems and the consistency and convergence behaviour of the numerical approach is shown. Tensile softening formulation using the concept of fracture energy is utilised for the nonlinear range. In this range, the approach is validated using the classical benchmark tests with pure tensile, split-tensile, combined shear-tensile and bending dominated push-over loading. The load–displacement behaviour and crack response were captured successfully, showing the proposed methodology can be used to quantify discrete cracks on large systems, such as dam monoliths, from initiation to significant damage levels.

A Probabilistic Autoencoder for Type Ia Supernova Spectral Time Series

We construct a physically parameterized probabilistic autoencoder (PAE) to learn the intrinsic diversity of Type Ia supernovae (SNe Ia) from a sparse set of spectral time series. The PAE is a two-stage generative model, composed of an autoencoder that is interpreted probabilistically after training using a normalizing flow. We demonstrate that the PAE learns a low-dimensional latent space that captures the nonlinear range of features that exists within the population and can accurately model the spectral evolution of SNe Ia across the full range of wavelength and observation times directly from the data. By introducing a correlation penalty term and multistage training setup alongside our physically parameterized network, we show that intrinsic and extrinsic modes of variability can be separated during training, removing the need for the additional models to perform magnitude standardization. We then use our PAE in a number of downstream tasks on SNe Ia for increasingly precise cosmological analyses, including the automatic detection of SN outliers, the generation of samples consistent with the data distribution, and solving the inverse problem in the presence of noisy and incomplete data to constrain cosmological distance measurements. We find that the optimal number of intrinsic model parameters appears to be three, in line with previous studies, and show that we can standardize our test sample of SNe Ia with an rms of 0.091 ± 0.010 mag, which corresponds to 0.074 ± 0.010 mag if peculiar velocity contributions are removed. Trained models and codes are released at https://github.com/georgestein/suPAErnova.

Iterative method for obtaining nonuniform grinding-induced residual stress distribution of silicon wafers based on global deformation

Grinding as the main thinning process for silicon wafers is widely used in chip manufacturing. The residual stress distribution is desired to be known to optimize the grinding process. In this paper, an iterative method for obtaining the nonuniform residual stress of ground silicon wafers was proposed. The deformation of ground silicon wafers was divided into two parts in which one part was large spherical deformation and the other was a small out-of-sphere deformation. The spherical deformation which was in the nonlinear range corresponded to an average stress which was obtained using the bisection method. The small out-of-sphere deformation corresponded to the stress variation which was obtained using the regularization method with continuity constraints. An iterative successive approximation process was conducted to address the nonlinear problem which was transformed into a local linear problem. The residual stress distribution of a ground silicon wafer was obtained successfully using the proposed method. Although the overall shape of the wafer deformation was approximately spherical, the residual stress value varied a lot with the crystal orientation of the silicon wafer. The stress values in the <110> orientations were much larger than those in the <100> orientations. The method could be used to evaluate the grinding process independently of the dimension sizes of ground silicon wafers. The proposed method in this paper is non-destructive and could be used to track the residual stress changes in the grinding process and the process parameters could be optimized accordingly.

Narrow-Gap Rheometry: A Novel Method for Measuring Cell Mechanics.

The viscoelastic properties of a cell cytoskeleton contain abundant information about the state of a cell. Cells show a response to a specific environment or an administered drug through changes in their viscoelastic properties. Studies of single cells have shown that chemical agents that interact with the cytoskeleton can alter mechanical cell properties and suppress mitosis. This envisions using rheological measurements as a non-specific tool for drug development, the pharmacological screening of new drug agents, and to optimize dosage. Although there exists a number of sophisticated methods for studying mechanical properties of single cells, studying concentration dependencies is difficult and cumbersome with these methods: large cell-to-cell variations demand high repetition rates to obtain statistically significant data. Furthermore, method-induced changes in the cell mechanics cannot be excluded when working in a nonlinear viscoelastic range. To address these issues, we not only compared narrow-gap rheometry with commonly used single cell techniques, such as atomic force microscopy and microfluidic-based approaches, but we also compared existing cell monolayer studies used to estimate cell mechanical properties. This review provides insight for whether and how narrow-gap rheometer could be used as an efficient drug screening tool, which could further improve our current understanding of the mechanical issues present in the treatment of human diseases.

High Sensing Accuracy Realisation With Millimetre/Sub-Millimetre Resolution in Optical Frequency Domain Reflectometer

By effectively suppressing the nonlinear sweep noise and random range of wavelength sweep in the optical frequency domain reflectometer, the theoretical spatial resolution and uniform sweep distribution are delivered for high sensing accuracy. A strain accuracy of ±0.51 μϵ is realised with a 5 mm sensing resolution, while the accuracy is ±5.89 μϵ with a 1 mm sensing resolution. Theoretical limitation between the strain accuracy and sensing resolution is further studied for the sub-millimetre resolution sensing. It is found that signal to noise ratio and frequency bandwidth of the calculated cross-correlation are critical factors in measuring accuracy. Increasing the sweep range can provide a better spatial frequency step for a high signal to noise ratio in the cross-correlation. With a 130 nm sweep range, the measurement accuracy is limited to ±19.31 μϵ with a 0.5 mm sensing resolution. Besides, for the long-distance sensing of 104 m, the measurement accuracy is ±8.72 μϵ with a 1 mm sensing resolution.

Designing and validating a robust adaptive neuromodulation algorithm for closed-loop control of brain states

Objective. Neuromodulation systems that use closed-loop brain stimulation to control brain states can provide new therapies for brain disorders. To date, closed-loop brain stimulation has largely used linear time-invariant controllers. However, nonlinear time-varying brain network dynamics and external disturbances can appear during real-time stimulation, collectively leading to real-time model uncertainty. Real-time model uncertainty can degrade the performance or even cause instability of time-invariant controllers. Three problems need to be resolved to enable accurate and stable control under model uncertainty. First, an adaptive controller is needed to track the model uncertainty. Second, the adaptive controller additionally needs to be robust to noise and disturbances. Third, theoretical analyses of stability and robustness are needed as prerequisites for stable operation of the controller in practical applications. Approach. We develop a robust adaptive neuromodulation algorithm that solves the above three problems. First, we develop a state-space brain network model that explicitly includes nonlinear terms of real-time model uncertainty and design an adaptive controller to track and cancel the model uncertainty. Second, to improve the robustness of the adaptive controller, we design two linear filters to increase steady-state control accuracy and reduce sensitivity to high-frequency noise and disturbances. Third, we conduct theoretical analyses to prove the stability of the neuromodulation algorithm and establish a trade-off between stability and robustness, which we further use to optimize the algorithm design. Finally, we validate the algorithm using comprehensive Monte Carlo simulations that span a broad range of model nonlinearity, uncertainty, and complexity. Main results. The robust adaptive neuromodulation algorithm accurately tracks various types of target brain state trajectories, enables stable and robust control, and significantly outperforms state-of-the-art neuromodulation algorithms. Significance. Our algorithm has implications for future designs of precise, stable, and robust closed-loop brain stimulation systems to treat brain disorders and facilitate brain functions.

Novel low frequency bionic vibration isolation structure

Inspired by the hind limbs of goats, a bio-inspired polygon vibration isolation structure with nonlinear stiffness and damping is proposed. The bionic mechanism consists of four bionic legs with different rods (as skeleton), 12 inclined tension springs (as muscle or tendon), a bearing platform, a base, and so on. A theoretical model is developed to characterize its stiffness nonlinearity through geometrical and mechanical analysis. Theoretical analysis shows that the bionic structure has nonlinear positive stiffness and large working range. The dynamic model of the structure is established based on the Lagrange principle, and the influence of various structural parameters on the vibration isolation performance of the structure was analyzed combined with ADAMS. Thanks to the unique bionic design, the device allows the stiffness and damping characteristics of the system to be adjusted by varying the structural parameters, resulting in excellent stability, high static and low dynamic stiffness, excellent vibration isolation performance, and good load carrying capacity without active control.

Surging Wind Turbine Simulations with a Free Wake Panel Method

We investigate the aerodynamics of a surging wind turbine with numerical simulations based on a free wake panel method. We start by demonstrating the method’s capability to simulate a plunging airfoil, which provides some insights that are later used to interpret results of a surging rotor. We then validate the method on a non-surging wind turbine and discuss the strengths and weaknesses of our approach. Next, we focus on the UNAFLOW case: a surging wind turbine which was modelled experimentally and with various numerical methods. Good agreement with experimental data is observed for amplitude and phase of the thrust with surge motion. For the first time, we achieve numerical results of a wind turbine wake that accurately reproduce experimentally verified effects of surging motion. Finally, we extend our simulations beyond the frequency range of the UNAFLOW experiments and reach results that do not follow a quasi-steady response. Using the plunging airfoil data, we justify the behavior observed in the non-linear range. Our work seeks to contribute a different method to the pool of results for the UNAFLOW case, while extending the analysis to conditions that have not been simulated before.

Interaction between breaking-induced vortices and near-bed structures. Part 1. Experimental and theoretical investigation

The present work describes the vortex–vortex interactions observed during laboratory experiments, where a single regular water wave is allowed to travel over a discontinuous rigid bed promoting the generation of both near-bed and surface vortices. While near-bed vortices are generated by the flow separation occurring at the bed discontinuity, surface vortices are induced by the wave breaking in conjunction with a breaking-induced jet. A ‘backward breaking’ (previously observed in the case of solitary waves) occurs at the air–water interface downstream of the discontinuity and generates a surface anticlockwise vortex that interacts with the near-bed clockwise vortex. With the vortex–vortex interaction influenced by many physical mechanisms, a point-vortex model, by which vortices evolve under both self-advection (in relation to both free surface and seabed) and mutual interaction, has been implemented to separately investigate the vortex- and wave-induced dynamics. The available data indicate that both self-advection and mutual interaction are the governing mechanisms for the downward motion of the surface vortex, with the effect of the breaking-induced jet being negligible. The same two mechanisms, combined with the mean flow, are responsible for the almost horizontal and oscillating path of the near-bed vortex. The investigation of the vortex paths allow us to group the performed tests into three distinct classes, each characterized by a specific range of wave nonlinearity. The time evolution of the main variables characterizing the vortices (e.g. circulation, kinetic energy, enstrophy, radius) and their maximum values increase with the wave nonlinearity, such dependences being described by synthetic best-fit formulas.

Mechanistic modeling and simulation of a complex low and high loading elution behavior of a polypeptide in cation exchange chromatography.

The mechanistic modeling of preparative liquid chromatography is still a challenging task. Nonideal thermodynamic conditions may require activity coefficients for the mechanistic description of preparative chromatography. In this work, a chromatographic cation exchange step with a polypeptide having a complex elution behavior in low and high loading situations is modeled. Model calibration in the linear range of the isotherm is done by applying counterion-induced linear gradient elution experiments between pH3.3 and 4.3. Inverse fitting with column loads up to 25mg/mLCV is performed for parameter estimation in the nonlinear range. The polypeptide elution peak shows an anti-Langmuirian behavior with fronting under low loading conditions and a switch to a Langmuirian behavior with increasing load. This unusual elution behavior could be described with an extended version of the sigmoidal Self-Association isotherm including two activity coefficients for the polypeptide and counterion in solution. The activity coefficient of the solute polypeptide shows a strong influence on the model parameters and is crucial in the linear and nonlinear range of the isotherm. The modeling procedure results in a unique and robust model parameter set that is sufficient to describe the complex elution behavior and allows modeling over the full isotherm range.

Graded Interlocks for Iontronic Pressure Sensors with High Sensitivity and High Linearity over a Broad Range.

Flexible pressure sensors that have high sensitivity, high linearity, and a wide pressure-response range are highly desired in applications of robotic sensation and human health monitoring. The challenge comes from the incompressibility of soft materials and the stiffening of microstructures in the device interfaces that lead to gradually saturated response. Therefore, the signal is nonlinear and pressure-response range is limited. Here, we show an iontronic flexible pressure sensor that can achieve high sensitivity (49.1 kPa-1), linear response (R2 > 0.995) over a broad pressure range (up to 485 kPa) enabled by graded interlocks of an array of hemispheres with fine pillars in the ionic layer. The high linearity comes from the fact that the pillar deformation can compensate for the effect of structural stiffening. The response-relaxation time of the sensor is <5 ms, allowing the device to detect vibration signals with frequencies up to 200 Hz. Our sensor has been used to recognize objects with different weights based on machine learning during the gripper grasping tasks. This work provides a strategy to make flexible pressure sensors that have combined performances of high sensitivity, high linearity, and wide pressure-response range.