Nonlinear dynamic behaviors and PID control of viscoelastic dielectric elastomer balloons

2021 ◽  
pp. 1045389X2110572
Author(s):  
Zhencai Xing ◽  
Huadong Yong
Keyword(s):  
Relaxation Time ◽  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Relaxation Times ◽  
Maxwell Model ◽  
Dielectric Elastomer ◽  
Strong Nonlinearity ◽  
Control Effect ◽  
Generalized Maxwell Model ◽  
Small Amplitude Oscillation

As a type of intelligent electroactive polymer, dielectric elastomer (DE) exhibits viscoelastic properties. It’s worth pointing out that the relaxation time has great significance for studying the mechanical behavior of viscoelastic polymer. In this paper, a generalized Maxwell model is used to describe the viscoelastic property of dielectric elastomer balloon. Meanwhile, a theoretical model with multiple relaxation times is used and the natural frequency of small amplitude oscillation is derived. Subsequently, the model is validated by comparing with experimental results. The model with double relaxation times can describe the deformation of the dielectric elastomer balloon effectively. Then the effect of relaxation time and shear modulus on the dynamic response of DE balloon is studied. Furthermore, the dielectric elastomer balloons in practical application exhibit the strong nonlinearity and the viscoelastic dissipation. Therefore, it is important to precisely control the dynamic response. The proportional-integral-differential (PID) controller in the form of nonlinear combination is adopted to control the above nonlinear dynamic systems actively. The results indicate that it is feasible to achieve desired control effect.

scholarly journals Dynamic Electromechanical Response of a Viscoelastic Dielectric Elastomer under Cycle Electric Loads

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Junjie Sheng ◽  
Yuqing Zhang
Keyword(s):  
Dynamic Response ◽  
Dynamic Stability ◽  
Relaxation Times ◽  
Excitation Frequency ◽  
Dielectric Elastomer ◽  
Time Dependent ◽  
Electric Load ◽  
Single Cycle ◽  
Set Up ◽  
Electric Loads

Dielectric elastomer (DE) is able to produce large electromechanical deformation which is time-dependent due to the viscoelasticity. In the current study, a thermodynamic model is set up to characterize the influence of viscoelasticity on the electromechanical and dynamic response of a viscoelastic DE. The time-dependent dynamic deformation, the hysteresis, and the dynamic stability undergoing viscoelastic dissipative processes are investigated. The results show that the electromechanical stability has strong frequency dependence; the viscoelastic DE can attain a larger stretch in the dynamic response than the quasistatic actuation. Furthermore, with the decreasing frequency of the applied electric load, the viscoelastic DE system will present dynamic stability evolution from an aperiodic motion to the quasiperiodic motion. The DE system may also experience a stability evolution from a single cycle motion to multicycle motion with the increasing relaxation times. The value and variation trend of the amplitude of the stretch are highly dependent on the excitation frequency and the relaxation time.

Stress Relaxation of Apples at Different Deformation Velocities and Temperatures

2019 ◽  
Vol 62 (1) ◽  
pp. 115-121 ◽  
Author(s):  
Zbigniew Stropek ◽  
Zbigniew Stropek ◽  
Krzysztof Golacki ◽  
Krzysztof Golacki
Keyword(s):  
Stress Relaxation ◽  
Impact Loading ◽  
Static Loading ◽  
Loading Condition ◽  
Relaxation Times ◽  
Maxwell Model ◽  
Peak Force ◽  
Force Response ◽  
Deformation Velocity ◽  
Generalized Maxwell Model

ABSTRACT. Stress relaxation tests on apples (‘Beni Shogun’ variety) were performed at different velocities in the range of 0.0002 to 1 m s-1 and at three temperatures (2°C, 10°C, and 20°C). The generalized Maxwell model was used to describe the experimental stress relaxation curves. The two relaxation times of the model decreased with an increase in the deformation velocity. The relaxation times were related to the processes of gas and liquid flows in the intercellular spaces. This research showed the critical velocity associated with the weakness of the apple structure to lie between deformation velocities of 0.0002 and 0.002 m s-1, where a rapid decrease in the two relaxation times occurred. An increase in the peak force response with increasing deformation velocity showed the viscoelastic behavior of apple flesh. The equilibrium modulus describing the material condition after deformation was much larger under the quasi-static loading condition than the impact loading condition at all deformation velocities. The temperature did not seem to affect the Maxwell model parameters and peak force response for all deformation velocities under both loading conditions. Keywords: Apple, Generalized Maxwell model, Impact loading, Quasi-static loading, Stress relaxation, Viscoelasticity.

scholarly journals Viscoelastic response of apple flesh in a wide range of mechanical loading rates

2018 ◽  
Vol 32 (3) ◽  
pp. 335-340 ◽  
Author(s):  
Zbigniew Stropek ◽  
Krzysztof Gołacki
Keyword(s):  
Relaxation Time ◽  
Impact Loading ◽  
Relaxation Times ◽  
Maxwell Model ◽  
Loading Conditions ◽  
Deformation Velocity ◽  
Time Order ◽  
Order Of Magnitude ◽  
Residual Force ◽  
The Impact

Abstract The cylindrical samples of ‘Beni Shogun’ apples cultivar in a range of deformation velocities from 0.0002 to 1 m s−1 were studied using stress relaxation tests. In the work, experimental courses of the force response were described via the Maxwell model, and the effects of deformation velocity on the Maxwell model parameters as well as the maximum and residual force were determined. The maximum force increased with the increase of the deformation velocity, which proved the response of apple flesh to be of viscoelastic nature. The residual force described the state of the material after the strain and was much higher under the quasi-static than impact loading conditions. The three relaxation times decreased with the increasing deformation velocity. For the shortest relaxation time (order of magnitude 0.1 s) there was a rapid decrease in the velocities under the quasi-static loading conditions and it remained on a steady and low level under the impact loading conditions. A definite limit was observed between the medium relaxation time (order of magnitude 1 s) for the lowest deformation velocity of 0.0002 m s−1 and the other relaxation times obtained at higher deformation velocities. The values of the longest relaxation time (order of magnitude 100 s) were much larger under the quasi-static than the impact loading conditions.

scholarly journals Biomechanics of pollen pellet removal by the honey bee

2021 ◽  
Vol 18 (181) ◽  
pp. 20210549
Author(s):  
Marguerite Matherne ◽  
Caroline Dowell-Esquivel ◽  
Oliver Howington ◽  
Olivia Lenaghan ◽  
Gabi Steinbach ◽  
...  
Keyword(s):  
Experimental Study ◽  
Shear Stress ◽  
Relaxation Time ◽  
Apis Mellifera ◽  
Honey Bee ◽  
Honey Bees ◽  
Relaxation Times ◽  
Maxwell Model ◽  
Viscoelastic Materials ◽  
Creep Tests

Honey bees ( Apis mellifera ) carry pollen back to their hive by mixing it with nectar and forming it into a pellet. The pellet must be firmly attached to their legs during flight, but also easily removable when deposited in the hive. How does the honey bee achieve these contrary aims? In this experimental study, we film honey bees removing pollen pellets and find they peel them off at speeds 2–10 times slower than their typical grooming speeds. Using a self-built pollen scraper, we find that slow removal speeds reduce the force and work required to remove the pellet under shear stress. Creep tests on individual pollen pellets revealed that pollen pellets are viscoelastic materials characterized by a Maxwell model with long relaxation times. The relaxation time enables the pellet to remain a solid during both transport and removal. We hope that this work inspires further research into viscoelastic materials in nature.

Correlation of Dynamic and Static Measurements on Rubberlike Materials

1952 ◽  
Vol 25 (4) ◽  
pp. 730-750
Author(s):  
R. D. Andrews
Keyword(s):  
Relaxation Time ◽  
Relaxation Times ◽  
Maxwell Model ◽  
Mathematical Structure ◽  
Individual Characteristics ◽  
Mathematical Methods ◽  
Approximate Methods ◽  
Static Modulus ◽  
The Individual ◽  
Rubberlike Materials

Abstract Dynamic and static measurements of rubberlike materials can be related in terms of a generalized Maxwell model which is assumed to represent the mechanical behavior of the system, the individual characteristics of the system being expressed by the nature of the relaxation time distribution of the model. Such properties as dynamic modulus and dynamic viscosity measured in experiments involving sinusoidal vibrations and static modulus measured in experiments of relaxation of stress at constant strain can be expressed by integrals involving the distribution of relaxation times. The distribution of relaxation times can, therefore, be calculated from experimental data of this sort by suitable mathematical methods. Because of the complexity of such calculations when carried out rigorously, the use of approximate methods is often desirable. A number of useful approximate relations can be derived by investigation of the mathematical structure of the integrals relating the distribution of relaxation times to the observed properties and by examination of the behavior of certain particular relaxation time distributions. Attempts to correlate dynamic and static data on the basis of this general theory by use of the approximate relations discussed have been reasonably successful.

scholarly journals T2 mapping of the peritumoral infiltration zone of glioblastoma and anaplastic astrocytoma

2021 ◽  
pp. 197140092198932
Author(s):  
Timo Alexander Auer ◽  
Maike Kern ◽  
Uli Fehrenbach ◽  
Yasemin Tanyldizi ◽  
Martin Misch ◽  
...  
Keyword(s):  
Relaxation Time ◽  
Isocitrate Dehydrogenase ◽  
Anaplastic Astrocytoma ◽  
T2 Mapping ◽  
Relaxation Times ◽  
Region Of Interest ◽  
World Health ◽  
High Grade ◽  
High Grade Gliomas ◽  
Health Organization

Purpose To characterise peritumoral zones in glioblastoma and anaplastic astrocytoma evaluating T2 values using T2 mapping sequences. Materials and methods In this study, 41 patients with histopathologically confirmed World Health Organization high grade gliomas and preoperative magnetic resonance imaging examinations were retrospectively identified and enrolled. High grade gliomas were differentiated: (a) by grade, glioblastoma versus anaplastic astrocytoma; and (b) by isocitrate dehydrogenase mutational state, mutated versus wildtype. T2 map relaxation times were assessed from the tumour centre to peritumoral zones by means of a region of interest and calculated pixelwise by using a fit model. Results Significant differences between T2 values evaluated from the tumour centre to the peritumoral zone were found between glioblastoma and anaplastic astrocytoma, showing a higher decrease in signal intensity (T2 value) from tumour centre to periphery for glioblastoma ( P = 0.0049 – fit-model: glioblastoma –25.02± 19.89 (–54–10); anaplastic astrocytoma –5.57±22.94 (–51–47)). Similar results were found when the cohort was subdivided by their isocitrate dehydrogenase profile, showing an increased drawdown from tumour centre to periphery for wildtype in comparison to mutated isocitrate dehydrogenase ( P = 0.0430 – fit model: isocitrate dehydrogenase wildtype –10.35±16.20 (–51) – 0; isocitrate dehydrogenase mutated 12.14±21.24 (–15–47)). A strong statistical proof for both subgroup analyses ( P = 0.9987 – glioblastoma R2 0.93±0.08; anaplastic astrocytoma R2 0.94±0.15) was found. Conclusion Peritumoral T2 mapping relaxation time tissue behaviour of glioblastoma differs from anaplastic astrocytoma. Significant differences in T2 values, using T2 mapping relaxation time, were found between glioblastoma and anaplastic astrocytoma, capturing the tumour centre to the peritumoral zone. A similar curve progression from tumour centre to peritumoral zone was found for isocitrate dehydrogenase wildtype high grade gliomas in comparison to isocitrate dehydrogenase mutated high grade gliomas. This finding is in accordance with the biologically more aggressive behaviour of isocitrate dehydrogenase wildtype in comparison to isocitrate dehydrogenase mutated high grade gliomas. These results emphasize the potential of mapping techniques to reflect the tissue composition of high grade gliomas.

scholarly journals Theoretical Effect of Temperature on Threshold in the Hodgkin-Huxley Nerve Model

1966 ◽  
Vol 49 (5) ◽  
pp. 989-1005 ◽  
Author(s):  
Richard Fitzhugh
Keyword(s):  
Relaxation Time ◽  
Relaxation Times ◽  
Giant Axon ◽  
Temperature Curve ◽  
Effect Of Temperature ◽  
Threshold Temperature ◽  
Ionic Conductances ◽  
And Shifts ◽  
The Right ◽  
Increasing Temperature

In the squid giant axon, Sjodin and Mullins (1958), using 1 msec duration pulses, found a decrease of threshold with increasing temperature, while Guttman (1962), using 100 msec pulses, found an increase. Both results are qualitatively predicted by the Hodgkin-Huxley model. The threshold vs. temperature curve varies so much with the assumptions made regarding the temperature-dependence of the membrane ionic conductances that quantitative comparison between theory and experiment is not yet possible. For very short pulses, increasing temperature has two effects. (1) At lower temperatures the decrease of relaxation time of Na activation (m) relative to the electrical (RC) relaxation time favors excitation and decreases threshold. (2) For higher temperatures, effect (1) saturates, but the decreasing relaxation times of Na inactivation (h) and K activation (n) factor accommodation and increased threshold. The result is a U-shaped threshold temperature curve. R. Guttman has obtained such U-shaped curves for 50 µsec pulses. Assuming higher ionic conductances decreases the electrical relaxation time and shifts the curve to the right along the temperature axis. Making the conductances increase with temperature flattens the curve. Using very long pulses favors effect (2) over (1) and makes threshold increase monotonically with temperature.

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