Developing viscoelastic contact models and selecting suitable creep function for spherical biological cells

2019 ◽  
Vol 64 (5) ◽  
pp. 571-590
Author(s):  
Moharram Habibnejad Korayem ◽  
Yousef Habibi Sooha ◽  
Zahra Rastgear
Keyword(s):  
Viscoelastic Model ◽  
Indentation Test ◽  
The Other ◽  
Cell Cortex ◽  
Cell Behavior ◽  
Creep Function ◽  
Biological Cells ◽  
Viscoelastic Models ◽  
Elasticity Module ◽  
Biological Liquid

Abstract In most contact theories, the most popular of which are the three models of Hertz, Derjaguin, Muller and Toporov (DMT) and Johnson, Kendall and Roberts (JKR), biological cells were considered as an elastic material which is not a proper assumption. The elastic assumption in the case of biological cells could lead to neglecting the loading history as a result of which the stresses and strains applied to the material would not be studied accurately. In this paper, developing the three mentioned elastic models into viscoelastic models, simulating and comparing them with empirical data obtained through the indentation test of the MCF-7 cancer cell showed that the viscoelastic state presents a better prediction of biological cell behavior compared to that of an elastic state. The selection of the suitable creep function for objects in contact is another issue that has a significant importance in the viscoelastic case and this was investigated. Different mechanical models of a cell were studied and simulated for all three named theories among which the creep function obtained from the Kelvin model, a parallel combination of spring-damper, simplified the simulation and gave more precise results for modeling due to the fact that the obtained results from this model are closer to experimental ones and simpler than other models. On the other hand, for a more exact prediction of cell behavior, this model was modified by an equivalent elasticity module which considered cell components instead of the cell cortex only. The results of the simulation confirmed that a new elasticity module can improve the accuracy of cell models. After choosing the suitable mechanical model for the cell, we scrutinized the capability of the developed theories in predicting the results for biological liquid environments. Although the results of the Hertz and DMT viscoelastic models are closer to experimental ones in comparison with viscoelastic JKR, neglecting adhesion makes their prediction in biological liquid environments weak and erroneous. Therefore, it can be concluded that the developed viscoelastic model of JKR is more accurate and has a better performance in different environments than the other mentioned models.

Identification of Nonlinear Viscoelastic Models of Flexible Polyurethane Foam From Uniaxial Compression Data

2016 ◽  
Vol 138 (2) ◽  
Author(s):  
Yousof Azizi ◽  
Patricia Davies ◽  
Anil K. Bajaj
Keyword(s):  
Uniaxial Compression ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Model Parameters ◽  
Viscoelastic Models ◽  
Nonlinear Viscoelastic ◽  
Compression Data ◽  
Computationally Intensive ◽  
Nonlinear Viscoelastic Model ◽  
Flexible Polyurethane

Flexible polyethylene foam is used in many engineering applications. It exhibits nonlinear and viscoelastic behavior which makes it difficult to model. To date, several models have been developed to characterize the complex behavior of foams. These attempts include the computationally intensive microstructural models to continuum models that capture the macroscale behavior of the foam materials. In this research, a nonlinear viscoelastic model, which is an extension to previously developed models, is proposed and its ability to capture foam response in uniaxial compression is investigated. It is hypothesized that total stress can be decomposed into the sum of a nonlinear elastic component, modeled by a higher-order polynomial, and a nonlinear hereditary type viscoelastic component. System identification procedures were developed to estimate the model parameters using uniaxial cyclic compression data from experiments conducted at six different rates. The estimated model parameters for individual tests were used to develop a model with parameters that are a function of strain rates. The parameter estimation technique was modified to also develop a comprehensive model which captures the uniaxial behavior of all six tests. The performance of this model was compared to that of other nonlinear viscoelastic models.

Characterization of the viscoelastic model of in vivo human posterior thigh skin using ramp-relaxation indentation test

2018 ◽  
Vol 30 (4) ◽  
pp. 293-307 ◽  
Author(s):  
Seyed Jamaleddin Mostafavi Yazdi ◽  
Kwang Soo Cho ◽  
Namcheol Kang
Keyword(s):  
Viscoelastic Model ◽  
Indentation Test ◽  
Posterior Thigh

scholarly journals Prediction of creep behavior of laminated woven fabric with adhesive interlining under low stress in the bias direction

2016 ◽  
Vol 87 (3) ◽  
pp. 285-295 ◽  
Author(s):  
Masayuki Takatera ◽  
Ken Ishizawa ◽  
KyoungOk Kim
Keyword(s):  
Creep Strain ◽  
Creep Behavior ◽  
Viscoelastic Model ◽  
Element Model ◽  
Woven Fabric ◽  
Creep Model ◽  
Creep Tests ◽  
Viscoelastic Models ◽  
Experimental Creep ◽  
The Face

The effect of adhesive interlining on the creep behavior of a woven fabric in the bias direction was investigated. Three-element viscoelastic models were used to approximate the creep behavior of a face fabric and adhesive interlining. The creep model of a laminated fabric comprised a six-element model in which two three-element models are connected in parallel with the three-element model. Creep tests were carried out using face fabrics, adhesive interlinings, and their laminated fabrics without and with bonding adhesive interlining by hanging samples in the 45° bias direction under their own weight for 7 days. Creep strains of face fabrics bonded with adhesive interlining were found to be weaker than those of the face fabrics. The creep behavior for the face and interlining fabrics could be approximated using the three-element viscoelastic model with appropriate parameters. The experimental creep behavior of a laminated fabric without bonding was similar to the theoretical behavior. However, the experimental creep of laminated fabrics with bonding interlining was less than the calculated creep, owing to the increase in stiffness due to the adhesive. By revising the six-element model with the strains just after hanging and for 2 days, it was possible to predict the creep strain over 7 days.

Optimization of a Viscoelastic Structure: The Seat-Belt Problem

1969 ◽  
Vol 36 (3) ◽  
pp. 565-572 ◽  
Author(s):  
W. Nachbar ◽  
J. B. Schipmo¨lder
Keyword(s):  
Seat Belt ◽  
Viscoelastic Model ◽  
Small Strain ◽  
The Body ◽  
Strain Rates ◽  
Maximum Displacement ◽  
Critical Displacement ◽  
Viscoelastic Models ◽  
Maximum Value ◽  
Linear Viscoelastic

Optimization of the parameters of elementary linear viscoelastic models is considered for the design of a lap seat belt in automobiles. The vehicle is assumed to stop abruptly on impact. The parameters are optimized to allow the speed of the vehicle before impact to have the largest permissible value consistent with constraints imposed for the safety of the user of the belt. The constraints chosen here are: (a) the maximum displacement of the body after impact is equal to or less than a prescribed critical displacement; (b) the forward speed of the body at the critical displacement does not exceed a prescribed maximum value; (c) the force exerted by the belt on the body during the motion following impact does not exceed a prescribed maximum value. It is found that the optimized Kelvin-Voigt viscoelastic model is nearly 40 percent more effective than the purely elastic material. It is nearly as effective as constant deceleration. An additional and advantageous property is proposed, moreover, for belts of viscoelastic materials. This is that the material should have a relatively low spring rate at relatively small strain rates. The optimized belts for the elementary viscoelastic models are shown to be quite stiff at low strain rates, however.

Identification of Nonlinear Viscoelastic Models of Flexible Polyurethane Foam From Uniaxial Compression Data

2012 ◽  
Author(s):  
Yousof Azizi ◽  
Patricia Davies ◽  
Anil K. Bajaj
Keyword(s):  
Uniaxial Compression ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Model Parameters ◽  
Viscoelastic Models ◽  
Nonlinear Viscoelastic ◽  
Compression Data ◽  
Computationally Intensive ◽  
Nonlinear Viscoelastic Model ◽  
Flexible Polyurethane

Flexible polyethylene foam, which is used in many engineering applications, exhibits nonlinear and viscoelastic behavior. To date, several models have been proposed to characterize the complex behavior of foams from the computationally intensive microstructural models to continuum models that capture the macroscale behavior of the foam materials. A nonlinear viscoelastic model, which is an extension of previously developed models, is proposed and its ability to capture foam response in uniaxial compression is investigated. It is assumed in the model that total stress is decomposed into the sum of a nonlinear elastic component, which is modeled by a higher order polynomial, and a nonlinear hereditary type viscoelastic component. System identification procedures are developed to estimate the model parameters using uniaxial compression data from experiments conducted at different rates. The performance of this model is compared to that of other nonlinear viscoelastic models.

Nonlinear Dynamic Viscoelastic Model for Osteoarthritic Cartilage Indentation Force

2011 ◽  
Author(s):  
A. Vidal-Lesso ◽  
E. Ledesma-Orozco ◽  
R. Lesso-Arroyo ◽  
L. Daza-Benitez
Keyword(s):  
Mechanical Properties ◽  
Soft Tissues ◽  
Mechanical Response ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Indentation Test ◽  
Maxwell Model ◽  
Relaxation Curve ◽  
Geometrical Parameters ◽  
Osteoarthritic Cartilage

Biomechanical properties and dynamic response of soft tissues as articular cartilage remains issues for attention. Currently, linear isotropic models are still used for cartilage analysis in spite of its viscoelastic nature. Therefore, the aim of this study was to propose a nonlinear viscoelastic model for cartilage indentation that combines the geometrical parameters and velocity of the indentation test with the thickness of the sample as well as the mechanical properties of the tissue changing over time due to its viscoelastic behavior. Parameters of the indentation test and mechanical properties as a function of time were performed in Laplace space where the constitutive equation for viscoelasticity and the convolution theorem was applied in addition with the Maxwell model and Hayes et al. model for instantaneous elastic modulus. Results of the models were compared with experimental data of indentation tests on osteoarthritic cartilage of a unicompartmental osteoarthritis cases. The models showed a strong fit for the axial indentation nonlinear force in the loading curve (R2 = 0.992) and a good fit for unloading (R2 = 0.987), while an acceptable fit was observed in the relaxation curve (R2 = 0.967). These models may be used to study the mechanical response of osteoarthritic cartilage to several dynamical and geometrical test conditions.

Uncertainty Analysis of a Finite Deformation Viscoelastic Model

2014 ◽  
Author(s):  
Paul Miles ◽  
Michael Hays ◽  
Ralph Smith ◽  
William S. Oates
Keyword(s):  
Finite Deformation ◽  
Viscoelastic Model ◽  
Large Field ◽  
Additional Insight ◽  
Viscoelastic Models ◽  
Rate Dependent ◽  
Different Types ◽  
Viscoelastic Effects ◽  
Insight Into ◽  
Hyperelastic Models

The viscoelasticity of the dielectric elastomer, VHB 4910, is experimentally characterized, modeled, and analyzed using uncertainty quantification. These materials are known for their large field induced deformation and applications in smart structures, although the rate dependent viscoelastic effects are not well understood. To address this issue, we first quantify hyperelastic and viscoelastic model uncertainty by comparing a finite deformation viscoelastic model to uni-axial rate dependent experiments. The utilization of Bayesian statistics is shown to provide additional insight into different viscoelastic processes within elastomers. This is demonstrated by coupling two hyperelastic models, an Ogden model and a nonaffine model, to different types of viscoelastic models.

Analysis of Fractional Viscoelastic Material With Mechanical Parameters Dependent on Random Temperature

2017 ◽  
Vol 3 (3) ◽  
Author(s):  
G. Alotta ◽  
N. Colinas-Armijo
Keyword(s):  
Epoxy Resin ◽  
Viscoelastic Material ◽  
Viscoelastic Model ◽  
Polymeric Materials ◽  
Random Variable ◽  
The Other ◽  
Mechanical Parameters ◽  
Simple Method ◽  
Different Temperatures ◽  
Probability Density Function Pdf

It is well known that mechanical parameters of polymeric materials, e.g., epoxy resin, are strongly influenced by the temperature. On the other hand, in many applications, the temperature is not known exactly during the design process and this introduces uncertainties in the prevision of the behavior also when the stresses are deterministic. For this reason, in this paper, the mechanical behavior of an epoxy resin is characterized by means of a fractional viscoelastic model at different temperatures; then, a simple method to characterize the response of the fractional viscoelastic material at different temperatures modeled as a random variable with assigned probability density function (PDF) subjected to deterministic stresses is presented. It is found that the first- and second-order statistical moments of the response can be easily evaluated only by the knowledge of the PDF of the temperature and the behavior of the parameters with the temperature. Comparison with Monte Carlo simulations is also performed in order to assess the accuracy and the reliability of the method.

Experimental Validation of Non-Conventional Viscoelastic Models via Equivalent Damping Estimates

2008 ◽  
Author(s):  
Giuseppe Catania ◽  
Silvio Sorrentino
Keyword(s):  
Damping Ratio ◽  
Viscoelastic Model ◽  
Measurement Data ◽  
Vibration Measurement ◽  
Modal Parameter ◽  
Structural Dynamic ◽  
General Validity ◽  
Integer Order ◽  
Equivalent Damping ◽  
Viscoelastic Models

Non-conventional rheological models based on non-integer order differential operators can be used to describe the viscoelastic behavior of materials, especially of polymers. These models are usually selected and then validated by means of creep and relaxation tests. However, engineers dealing with structural dynamic problems may need to obtain model identification from vibration measurement data. In this case, however, the direct identification of an optimal set of parameters of a viscoelastic model from time or frequency domain measurements is a difficult task, especially if the structural dissipative contributions are slight. In this paper, an indirect approach is adopted, based on the concept of damping ratio. When dealing with standard linear viscous dissipative models, a damping ratio modal parameter ζn can be analytically defined and experimentally estimated. But this theoretical parameter shows a dependency from the modal frequency that may dramatically fail in fitting the experimental data. On the contrary, it is known that a better agreement between theory and experiments can be achieved by means of non-integer order differential models, even though in this case analytical expressions for ζn are difficult to find. To overcome this difficulty, a method of general validity for viscoelastic models is developed, based on the concept of equivalent damping ratio and on the circle-fit technique. The proposed method is applied to experimental damping estimates from plane flexural vibrations of clamped-free beams, obtained from specimens of different size made of materials such as Polyethylene, Polyvinyl-chloride and Delrin.

scholarly journals Formins specify membrane patterns generated by propagating actin waves

2020 ◽  
Vol 31 (5) ◽  
pp. 373-385 ◽  
Author(s):  
Mary Ecke ◽  
Jana Prassler ◽  
Patrick Tanribil ◽  
Annette Müller-Taubenberger ◽  
Sarah Körber ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Pattern Formation ◽  
The Other ◽  
Cell Cortex ◽  
Actin Waves

Actin waves beneath the membrane of Dictyostelium cells separate two distinct areas of the cell cortex. Upon wave propagation, one type of area is converted into the other. We show that specific formins are recruited to different areas of the wave landscape and use these actin-polymerizing machines to analyze the dynamics of pattern formation.

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