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Mathematical Modeling and Analysis of Soft Tissue Viscoelasticity and Dielectric Relaxation
Published in A. Bakiya, K. Kamalanand, R. L. J. De Britto, Mechano-Electric Correlations in the Human Physiological System, 2021
A. Bakiya, K. Kamalanand, R. L. J. De Britto
The viscoelastic properties of biological tissues are usually modeled as a combination of mechanical elements such as the spring and dashpot as it provides a simple and efficient representation (Zhang et al., 2007). The classical models which describe the linear viscoelastic behavior are the Maxwell model, Kelvin–Voigt model, and the standard linear solid model. These models are developed using the serial and parallel combination of springs and dashpots (Fung, 2013). Later, the fractional calculus was introduced into viscoelastic models. A modified Kelvin–Voigt model consisting of a spring in parallel to a dashpot with the stress in the dashpot equal to the fractional derivative of order “α” of the strain. This model is known as the Kelvin–Voigt fractional derivative model which incorporates the fractional derivative in the Kelvin–Voigt model (Caputo et al., 2011; Kiss et al., 2004).
Modeling in Cellular Biomechanics
Published in Joseph D. Bronzino, Donald R. Peterson, Biomedical Engineering Fundamentals, 2019
Alexander A. Spector and Roger Tran-Son-Tay
eret et al. (1988) analyzed the micropipette experiment with endothelial cells. e cell was interpreted as a linear elastic incompressible isotropic half-space, and the pipette was considered as an axisymmetric rigid punch. is approach was later extended (Sato et al., 1990) to consider the cell as a linear viscoelastic incompressible material obeying the standard linear solid model. Haider and Guilak (2002) have applied an axisymmetric boundary integral model to estimate elastic parameters of chondrocytes, assuming the cell to have the shape of a nite sphere. Baaijens et al. (2005) have applied the nite element method to analyze the micropipette aspiration experiment with chondrocytes by assuming them to be nonlinear viscoelastic and biphasic. Zhou et al. (2005) have developed a nite element analysis of the micropipette experiment in the case of large viscoelastic deformations where the cell was treated as a standard neo-Hookean viscoelastic solid. Spector et al. (1998) analyzed the application of the micropipette to a cylindrical cochlear outer hair cell. e cell composite membrane
Rethinking and researching the physical meaning of the standard linear solid model in viscoelasticity
Published in Mechanics of Advanced Materials and Structures, 2022
In this section, the theoretical background for demonstrating the physical meanings of the parameters of SLSMMaxwell will be presented. Three different perspectives will be respectively used for the demonstration, and it can be seen that those three different perspectives will lead to the same conclusion. One perspective is based on the viscoelastic behaviors in the loading process. The other two perspectives are based on the viscoelastic behaviors in the stress relaxation and creep processes . Please see Part A of the supplementary material for an introduction to the loading and stress relaxation processes in the stress relaxation test, and Part B of the supplementary material for an introduction to the loading and creep processes in the creep test. Stress relaxation and creep tests are two conventional and standard methods for evaluating the viscoelastic properties of materials. In literature, some novel techniques for this purpose have been proposed. For example, a novel analytical technique termed i-Rheo for evaluating the materials’ linear viscoelastic properties over the widest possible range of frequencies has been proposed [74, 127, 128]. The main advantage and feature of this novel technique are that it is simple and free from prescribed assumptions and models, and its evaluation is based on analyzing the Fourier transforms of experimental data involving both the time-dependent stress and strain functions excited using a simple step strain input. This technique can be widely used to analyze data obtained through various apparatuses, such as conventional material testing systems and atomic force microscopy [74, 128]. The author of the present paper believes that this kind of new concept can also be useful to demonstrate the physical meanings of classical viscoelastic models such as the standard linear solid model. In this paper, the conventional loading, stress relaxation and creep processes will be used for the demonstration.