Viscoelastic Creep Compliance Using Prony Series and Spectrum Function Approach

Simsiriwong, Jutima; Sullivan, Rani W.; Hilton, Harry H.

doi:10.1007/978-1-4614-4241-7_21

Cited by 5 publications

(5 citation statements)

References 11 publications

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“…For crosslinked polymers at room temperature, there is no Newtonian flow, and thus the creep can be fully recovered [19]. Therefore, the creep compliance can be described mathematically by a constant term and the Prony series [20]:…”

Section: Viscoelastic Creepingmentioning

confidence: 99%

SU-8 as a Torsional Spring: Viscoelastic Creeping and Closed Loop Control

Hierold

2015

J. Microelectromech. Syst.

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The torsional viscoelastic creeping and recovery of an SU-8 spring is reported by studying the deflection angle variation of a vertical comb-drive actuator suspended by an SU-8 spring at three different stress levels. A maximum creep of 0.43°(corresponding to a relative change of strain of 5.7%) is observed under a constant stress of 8.3 MPa in 1 h (V = 22.7 V). A capacitive readout circuit is designed to sense the torsional deflection of the comb-drive actuator. The circuit is capable of actuating and sensing the capacitance change by the same combdrives with a resolution of 0.03°(corresponding to a capacitance resolution of 0.05 pF). The readout capacitance is then used as the input variable for a proportional-integral (PI) controller in order to eliminate the time and load dependent drift by creeping of the SU-8 spring. The PI controller is tuned by the Ziegler-Nichols method and has a settling time of ∼2.3 s for the output. Compared with the open loop deflection of 0.43°, the closed-loop deflection is reduced by a factor of 7 down to 0.06°. This controller error is prominent at high actuation voltages, and is attributed to the actuator's lateral and vertical crosssensitivity. [2014-0124]

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Section: Viscoelastic Creepingmentioning

confidence: 99%

SU-8 as a Torsional Spring: Viscoelastic Creeping and Closed Loop Control

Hierold

2015

J. Microelectromech. Syst.

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“…At least 10 replicates were tested for each sample. The creep compliance C(t) was modelled according to the generalized Kelvin model (GKM) [125] as:…”

Section: Creep Behaviormentioning

confidence: 99%

Lodging Variability in Sorghum Stalks Is Dependent on the Biomechanical and Chemical Composition of the Stalk Rinds

Mengistie,

Bokros,

DeBolt

et al. 2024

Crops

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Stalk lodging contributes to significant crop yield losses. Therefore, understanding the biomechanical strength and structural rigidity of grain stalks can contribute to improving stalk lodging resistance in crops. From the structural constituents of the stalk, the rind provides the principal structure, supporting cells against tension and bending loads. In this work, the biomechanical and viscoelastic behavior of the rind from the internodes of two sweet sorghum varieties (Della and REDforGREEN (RG)), grown in two different growing seasons, were evaluated by three-point micro-bending tests using a dynamic mechanical analyzer (DMA). In addition, the chemical composition of rinds and the microfibril angle (MFA) of the cell wall were determined using XRD. The results revealed that the biomechanical behavior of Della varieties was stiffer and more resistant to loads than that of RG varieties. Two features of the rind biomechanical properties, flexural modulus (FM) and flexural strength (FS), showed a significant reduction for RG. Particularly, a reduction in FS of 16–37% and in FM of 22–41% were detected for RG1. Changes in the stalks’ rind biomechanical properties were attributed to cell wall components. Total lignin and glucan/cellulose contents were positively correlated with the FM and FS of the rind. Subsequently, an increase in the two cell wall components drove an increase in stiffness. Furthermore, the MFA of the rind was also found to influence the rind strength.

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“…More practical, but still operationally difficult, forms of (21) have been formulated in [61], [66], [67], [88] where they have been applied to creep test data. The stochastic functions describing stresses, strains, moduli, etc., are represented by simpler and mathematically more manageable forms consisting of single PDF rather than the 2N distinct PDFs of (21).…”

Section: Statistical and Probability Issuesmentioning

confidence: 99%

Uncertainty in Characterizations of Isotropic Linear Viscoelastic Shear and Bulk Moduli from 1 - D Tensile Experiments

Michaeli¹,

Shtark²,

Grosbein³

et al. 2014

55th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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Previous experiments at constant strain rates, while valuable in their own right, indicated that relaxation experiments at nominally constant strains are more conducive to obtaining data over numerous time decades in order to establish proper moduli/compliances, which cover the entire time range from instantaneous to fully relaxed moduli. The purpose of this paper, then, is to report on a series of relaxation experiments in order to produce high fidelity characterization of the statistical properties of viscoelastic materials, such as relaxation moduli, creep compliances, times to achieve constant strains, etc. Photometric, load cell, extensometers and accelerometer equipment was employed for data harvesting. Beta probability density functions with time dependent parameters were used to best describe the statistics as they answer the need to represent the data in a finite interval. A new analytical protocol for material determination, called the direct numerical calculation of viscoelastic moduli (DVM), has been developed and tested. Various protocols to determine the actual time to complete experimental loading phases are formulated as well as simple dynamic experiments for evaluating instantaneous moduli. Parallel to the above development the instantaneous modulus is determined from separate dynamic experiments and its statistical results are combined with 1 Copyright© the quasi-static experimental statistical data, thus providing time dependent probability density functions covering the entire positive time domain t ≥ 0. The time when the loading cycle ends is calculated from extensometers and its non-trivial influence on the characterization process is evaluated.It is shown that a stochastic elastic/viscoelastic correspondence principle can only be formulated based on integral transforms, since the constitutive relations are no longer of the convolution type. However, its utility for purposes of analysis of stress and strains is severely limited compared deterministic EVCPs because of the complicated non-convolution type constitutive relations.

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Viscoelastic Creep Compliance Using Prony Series and Spectrum Function Approach

Cited by 5 publications

References 11 publications

SU-8 as a Torsional Spring: Viscoelastic Creeping and Closed Loop Control

SU-8 as a Torsional Spring: Viscoelastic Creeping and Closed Loop Control

Lodging Variability in Sorghum Stalks Is Dependent on the Biomechanical and Chemical Composition of the Stalk Rinds

Uncertainty in Characterizations of Isotropic Linear Viscoelastic Shear and Bulk Moduli from 1 - D Tensile Experiments

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