A Note on the Reduced Creep Function Corresponding to the Quasi-Linear Visco-Elastic Model Proposed by Fung

1994 ◽  
Vol 116 (3) ◽  
pp. 373-375 ◽  
Author(s):  
L. J. M. G. Dortmans ◽  
A. A. F. van de Ven ◽  
A. A. H. J. Sauren
Keyword(s):  
Relaxation Function ◽  
Relaxation Spectrum ◽  
Biological Tissues ◽  
Elastic Behavior ◽  
Creep Function ◽  
Elastic Model ◽  
Soft Biological Tissues ◽  
Consistent Formulation

For description of the visco-elastic behavior of soft biological tissues, Fung proposed a visco-elastic model formulated in terms of a relaxation function and corresponding relaxation spectrum. For the corresponding creep function, Fung proposed an expression which needs correction to obtain a consistent formulation. This creep function and the corresponding creep spectrum are derived in this note.

Large Deformation Analysis of Some Soft Biological Tissues

1981 ◽  
Vol 103 (2) ◽  
pp. 73-78 ◽  
Author(s):  
H. Demiray
Keyword(s):  
Soft Tissues ◽  
Biological Tissues ◽  
Deformation Analysis ◽  
Elastic Model ◽  
Soft Biological Tissues ◽  
Large Deformation Analysis ◽  
Vulcanized Rubber ◽  
Nonlinear Stress ◽  
Physiological Structure ◽  
Theoretical Results

Due to physiological structure of most of the soft biological tissues, measurable stresses develop after the specimen has been stretched to many hundreds of percent of its relaxed length. Therefore, the nonlinear stress-strain relations developed for vulcanized rubber cannot be applied to soft tissues, which are constitutionally much more nonlinear than other engineering materials. In this article, using two different elastic models proposed for elastic soft tissues, simple elongation of a cylindrical bar and the inflation of a spherical thick shell, which is deemed to be a model for a left venticle, are studied and the material coefficients characterizing the elastic model are obtained via comparing theoretical results with existing experiments on tissues. Furthermore, the elastic stiffnesses which are very important for physiologists and cardiologists are discussed and the consistency of the result with experiments are indicated.

Indentation of Nonlinearly Viscoelastic Solids

2007 ◽  
Vol 1049 ◽  
Author(s):  
Michelle L Oyen
Keyword(s):  
Biological Tissues ◽  
Constant Load ◽  
Strain Level ◽  
Indentation Creep ◽  
Creep Function ◽  
Flat Punch ◽  
Viscoelastic Solids ◽  
Experimental Conditions ◽  
Soft Biological Tissues ◽  
Analytical Approaches

AbstractMuch recent attention has been focused on the indentation of linearly viscoelastic solids, and analysis techniques have been developed for polymeric material characterization. However, there has been relatively little progress made in the development of analytical approaches for indentation of nonlinearly viscoelastic materials. Soft biological tissues tend to exhibit responses which are nonlinearly viscoelastic and are frequently modeled using a decomposition of the relaxation or creep function into a product of two functions, one time-dependent and the other stress- or strain-level dependent. Consideration here is for soft biological tissue-like responses, exhibiting approximately quadratic stress-strain behavior, which can be alternatively cast as linear dependence of elastic modulus on strain level. An analytical approach is considered in the context of indentation problems with flat punch, spherical and conical indenter shapes. Hereditary integral expressions are developed and solved for typical indentation experimental conditions including indentation creep, load-relaxation and monotonic constant load- or displacement-rate tests. Primary emphasis is on the deconvolution of material and geometrical nonlinearities during an indentation experiment. The simple analytical expressions that result from this analysis can be implemented for indentation characterization of soft biological tissues without the need for computationally- intensive inverse finite element approaches.

Propagation of surface acoustic waves in the models of soft biological tissues

1992 ◽  
Vol 25 (7) ◽  
pp. 814
Author(s):  
Vladimir V. Shorokhov ◽  
Vadim N. Voronkov ◽  
Alexander N. Klishko
Keyword(s):  
Acoustic Waves ◽  
Surface Acoustic Waves ◽  
Biological Tissues ◽  
Soft Biological Tissues

Application of bandlimited anelastic models to wave propagation in highly attenuative media

1995 ◽  
Vol 85 (5) ◽  
pp. 1359-1372
Author(s):  
Hsi-Ping Liu
Keyword(s):  
Wave Propagation ◽  
Quality Factor ◽  
Lower Limit ◽  
Relaxation Function ◽  
Function Approach ◽  
Creep Function ◽  
Frequency Range ◽  
Quality Factors ◽  
Low Frequencies ◽  
Near Surface

Abstract Because of its simple form, a bandlimited, four-parameter anelastic model that yields nearly constant midband Q for low-loss materials is often used for calculating synthetic seismograms. The four parameters used in the literature to characterize anelastic behavior are τ1, τ2, Qm, and MR in the relaxation-function approach (s1 = 1/τ1 and s2 = 1/τ2 are angular frequencies defining the bandwidth, MR is the relaxed modulus, and Qm is approximately the midband quality factor when Qm ≫ 1); or τ1, τ2, Qm, and MR in the creep-function approach (s1 = 1/τ1 and s2 = 1/τ2 are angular frequencies defining the bandwidth, and Qm is approximately the midband quality factor when Qm ≫ 1). In practice, it is often the case that, for a particular medium, the quality factor Q(ω0) and phase velocity c(ω0) at an angular frequency ω0 (s1 < ω0 < s2; s1 < ω0 < s2) are known from field measurements. If values are assigned to τ1 and τ2 (τ2 < τ1), or to τ1 and τ2 (τ2 < τ1), then the two remaining parameters, Qm and MR, or Qm and MR, can be obtained from Q(ω0). However, for highly attenuative media, e.g., Q(ω0) ≦ 5, Q(ω) can become highly skewed and negative at low frequencies (for the relaxation-function approach) or at high frequencies (for the creep-function approach) if this procedure is followed. A negative Q(ω) is unacceptable because it implies an increase in energy for waves propagating in a homogeneous and attenuative medium. This article shows that given (τ1, τ2, ω0) or (τ1, τ2, ω0), a lower limit of Q(ω0) exists for a bandlimited, four-parameter anelastic model. In the relaxation-function approach, the minimum permissible Q(ω0) is given by ln [(1 + ω20τ21)/(1 + ω20τ22)]/{2 arctan [ω0(τ1 − τ2)/(1 + ω20τ1τ2)]}. In the creep-function approach, the minimum permissible Q(ω0) is given by {2 ln (τ1/τ2) − ln [(1 + ω20τ21)/(1 + ω20τ22)]}/{2 arctan [ω0(τ1 − τ2)/(1 + ω20τ1τ2)]}. The more general statement that, for a given set of relaxation mechanisms, a lower limit exists for Q(ω0) is also shown to hold. Because a nearly constant midband Q cannot be achieved for highly attenuative media using a four-parameter anelastic model, a bandlimited, six-parameter anelastic model that yields a nearly constant midband Q for such media is devised; an expression for the minimum permissible Q(ω0) is given. Six-parameter anelastic models with quality factors Q ∼ 5 and Q ∼ 16, constant to 6% over the frequency range 0.5 to 200 Hz, illustrate this result. In conformity with field observations that Q(ω) for near-surface earth materials is approximately constant over a wide frequency range, the bandlimited, six-parameter anelastic models are suitable for modeling wave propagation in highly attenuative media for bandlimited time functions in engineering and exploration seismology.

Effect of Segmented Electrodes on Piezo-Elastic and Piezo-Aero-Elastic Responses of Generator Plates

2009 ◽  
Author(s):  
Carlos De Marqui ◽  
Alper Erturk ◽  
Daniel J. Inman
Keyword(s):  
Electrical Power ◽  
Elastic Behavior ◽  
Elastic Model ◽  
Fe Model ◽  
Aeroelastic Response ◽  
Aerodynamic Model ◽  
Frequency Excitation ◽  
Elastic Responses ◽  
Electrical Power Output ◽  
Tip Mass

In this paper, the use of segmented electrodes is investigated to avoid cancellation of the electrical outputs of the torsional modes in energy harvesting from piezo-elastic and piezo-aero-elastic systems. The piezo-elastic behavior of a cantilevered plate with an asymmetric tip mass under base excitation is investigated using an electromechanically coupled finite element (FE) model. Electromechanical frequency response functions (FRFs) are obtained using the coupled FE model both for the continuous and segmented electrodes configurations. When segmented electrodes are considered torsional modes also become significant in the resulting electrical FRFs, improving broadband (or varying-frequency excitation) performance of the generator plate. The FE model is also combined with an unsteady aerodynamic model to obtain the piezo-aero-elastic model. The use of segmented electrodes to improve the electrical power generation from aeroelastic vibrations of plate-like wings is investigated. Although the main goal here is to obtain the maximum electrical power output for each airflow speed (both for the continuous and segmented electrode cases), piezoelectric shunt damping effect on the aeroelastic response of the generator wing is also investigated.

Spherical indentation load-relaxation of soft biological tissues

2006 ◽  
Vol 21 (8) ◽  
pp. 2003-2010 ◽  
Author(s):  
Jason M. Mattice ◽  
Anthony G. Lau ◽  
Michelle L. Oyen ◽  
Richard W. Kent
Keyword(s):  
Costal Cartilage ◽  
Kidney Tissue ◽  
Biological Tissues ◽  
Indentation Load ◽  
Spherical Indentation ◽  
Load Relaxation ◽  
Soft Biological Tissues ◽  
Long Time ◽  
Constant Displacement ◽  
Soft Biological Materials

Elastic-viscoelastic correspondence was used to generate displacement–time solutions for spherical indentation testing of soft biological materials with time-dependent mechanical behavior. Boltzmann hereditary integral operators were used to determine solutions for indentation load-relaxation following a constant displacement rate ramp. A “ramp correction factor” approach was used for routine analysis of experimental load-relaxation data. Experimental load-relaxation tests were performed on rubber, as well as kidney tissue and costal cartilage, two hydrated soft biological tissues with vastly different mechanical responses. The experimental data were fit to the spherical indentation ramp-relaxation solutions to obtain values of short- and long-time shear modulus and of material time constants. The method is used to demonstrate linearly viscoelastic responses in rubber, level-independent indentation results for costal cartilage, and age-independent indentation results for kidney parenchymal tissue.

scholarly journals Численное моделирование миграции фотонов в однородных и неоднородных цилиндрических фантомах

2020 ◽  
Vol 128 (6) ◽  
pp. 832
Author(s):  
А.Ю. Потлов ◽  
С.В. Фролов ◽  
С.Г. Проскурин
Keyword(s):  
Radiation Transfer ◽  
Biological Tissues ◽  
Photon Density ◽  
Radiation Transfer Equation ◽  
Scattering Media ◽  
Soft Biological Tissues ◽  
Photon Diffusion ◽  
Low Coherence ◽  
The Brain ◽  
Pulsed Irradiation

The specific features of photon diffusion of low-coherence pulsed irradiation in phantoms of soft biological tissues (blood-saturated tissues of the brain, breast, etc.) are described. The results of photon migration simulation using the Diffusion Approximation to the Radiation Transfer Equation (RTE) are compared with ones of the Monte Carlo simulations. It has been confirmed that the Photon Density Normalized Maximum (PDNM) moves towards the center of the investigated object in case of relatively uniform and strongly scattering media. In the presence of inhomogeneities, type of the PDNM motion changes drastically. Presence of an absorbing inhomogeneity in the medium directs trajectory of the PDNM motion of towards the point symmetric to the inhomogeneity relative to the geometric center of the investigated object. In case of scattering the PDNM moves toward the direction of the center of the scattering inhomogeneity.

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