Visco-Elasticity of Passive Cardiac Muscle

1980 ◽  
Vol 102 (1) ◽  
pp. 57-61 ◽  
Author(s):  
J. G. Pinto ◽  
P. J. Patitucci
Keyword(s):  
Mechanical Behavior ◽  
Cardiac Muscle ◽  
Heart Muscle ◽  
Relaxation Times ◽  
Continuous Distribution ◽  
Biological Tissues ◽  
Constitutive Law ◽  
Strain Behavior ◽  
Standard Linear Solid ◽  
Standard Linear

A quantitative mechanical description of the heart organ requires information on the mechanical behavior of its muscle in reasonable unity and completeness. In this respect, a fundamental constitutive law for soft biological tissues was proposed by Fung in 1972. This article presents evidence to show that Fung’s law is a useful law to describe the mechanical behavior of heart muscle in the unstimulated (diastolic) state with sufficient generality. A visco-elastic relaxation phenomenon is studied in the isolated cardiac muscle of cat and rabbit with the purpose of constructing a mathematical model for relaxation. Experimental results show that passive relaxation behavior of heart muscle can be adequately described by a generalized standard linear solid with a continuous distribution of relaxation times. The form of the relaxation function devised permits the application of linear visco-elasticity theory to the nonlinear cardiac muscle. The relaxation model is used to predict the force-length (stress-strain) behavior of papillary muscle with reasonable accuracy.

Identifying the parameters of viscoelastic model for a gel-type material as representative of cardiac muscle in dynamic tests

2021 ◽  
pp. 095441192110258
Author(s):  
Majid Siami ◽  
Kamal Jahani ◽  
Mousa Rezaee
Keyword(s):  
Cardiac Muscle ◽  
Heart Muscle ◽  
Experimental Studies ◽  
Type Material ◽  
Solid Model ◽  
Dynamic Tests ◽  
Leadless Pacemaker ◽  
Standard Linear Solid Model ◽  
Standard Linear Solid ◽  
Standard Linear

In this paper, mechanical parameters of a calf heart muscle are identified and a gel-type material as the representative of the cardiac muscle in dynamic tests is introduced. The motivation of this study is to introduce a replacement material of the heart muscle to use in experimental studies of the leadless pacemaker. A particular test setup is developed to capture the experimental data based on the stress relaxation test method where its outputs are time histories of the force and displacement. The standard linear solid model is used for mathematical modeling of the heart muscle sample and a gel-type material specimen namely α-gel. Five tests with different strain history [Formula: see text] are performed by regarding and disregarding the influence of the initial ramp of the loading. The mechanical parameters of the standard linear solid model were identified with precise curve fitting. Consideration of the initial ramp significantly influences the consequences and they are so close to their experimental counterparts. The identified parameters of the standard linear solid model by regarding the influence of the initial ramp for the gel-type material are within an acceptable range for the viscoelastic properties of the calf heart tissue. These results show that the gel-type material has the potential to represent the cardiac muscle in the leadless pacemaker experimental studies. Dynamic mechanical analysis is used to characterize the dynamic viscoelastic properties for the gel by utilizing the identified parameters with taking into account the initial ramp in the frequency domain. Results show that Storage modulus, Loss modulus, and Loss tangent are strongly frequency-dependent especially at low-frequency around the heartbeat frequency range (0–2 Hz).

A Nonlinear Viscoelastic Model for Polyester Mooring Line Analysis

2011 ◽  
Author(s):  
J. W. Kim ◽  
J. H. Kyoung ◽  
A. Sablok ◽  
K. Lambrakos
Keyword(s):  
Dynamic Stiffness ◽  
Relaxation Times ◽  
Viscoelastic Model ◽  
Line Tension ◽  
Mooring Line ◽  
Prony Series ◽  
Nonlinear Viscoelastic ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Nonlinear Viscoelastic Model

A viscoelastic model considering multiple relaxation times and nonlinearity in dynamic stiffness has been developed. The model is based on the Maxwell-Wiechert model, which is an extension of an earlier model based on the standard linear solid (SLS) model. The time-dependent elastic modulus of polyester rope is represented by a 4-term Prony series (MW4 model). Relaxation times and coefficients of the Prony series have been determined from test data of dynamic stiffness at different loading periods. Nonlinearity in dynamic stiffness is considered by iteratively adjusting the dynamic stiffness of polyester rope based on the calculated mean load on the rope. The developed model has been applied in the global performance analysis of a Spar platform moored in deep water. Platform offset and mooring-line tension comparisons between the SLS and the MW4 models are given for intact and broken mooring-line cases.

Mechanical Characterization of a Freestanding Polyvinyl Alcohol Hydrogel Membrane

2008 ◽  
Author(s):  
Edgar J. Montiel ◽  
Kai-Tak Wan
Keyword(s):  
Polyvinyl Alcohol ◽  
Biological Tissues ◽  
Material Strength ◽  
Hydrogel Membranes ◽  
Hydrogel Membrane ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Deformation Test

The following study presents two methods established for characterizing the mechanical properties of polyvinyl alcohol hydrogel membranes. The first one, an instant deformation test with an automated machine allowed the determination of the elastic properties of the material, while the second permitted the determination of the viscoelastic properties with the use of the standard linear solid model while confirming the previously found elastic results. This is not trivial as clearly old fashioned tests such as the ASTM standard tension test where grips are used to hold the sample are not feasible to perform due to the fragile characteristics of this kind material that resemble delicate biological tissues. The results obtained are consistent with previous publications, where different methods where used, but an increase in the material strength was also found as the number of freezing/thawing cycles increased.

scholarly journals Mechanical Behavior of Axonal Microtubules; the Effect of Fluid on the Rupture of Axonal Microtubules

2018 ◽  
Author(s):  
Farid Manuchehrfar ◽  
Amir Shamloo
Keyword(s):  
Mechanical Behavior ◽  
Tau Protein ◽  
Random Number ◽  
Average Length ◽  
Tau Proteins ◽  
Particle Dynamic ◽  
Vital Importance ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Cross Links

AbstractAxonal microtubules are dynamically instable bundles in the interior part of the axon. The dynamics of these bundles are of vital importance in the behavior of axon such as their degeneration. Each axon typically contains 10~100 microtubule bundles with average length of 4μm. These bundles are coated with cytoplasm and are cross linked with random number of tau proteins. In some circumstances such as acceleration or deceleration of head in space or during the strike, they are placed in tension which may cause rupture of these bundles or disconnection of tau protein cross links. Mechanical behavior and rupture modality of microtubule bundles are becoming more and more important recently. In our model, viscoelastic microtubule bundles constituted from several discrete masses connected to the neighboring mass with a standard linear solid (SLS), a spring damper model. In addition we take into account the effect of cytoplasm by Dissipative Particle Dynamic (DPD) to investigate the rupture nature and mechanical behavior of these bundles and the effect of cytoplasm on their mechanical behavior. We obtain these results for various amounts of suddenly applied end forces to the group of axonal microtubule bundles.

A Triboelastic Model for the Cyclic Mechanical Behavior of Filled Vulcanizates

1995 ◽  
Vol 68 (4) ◽  
pp. 660-670 ◽  
Author(s):  
V. A. Coveney ◽  
D. E. Johnson ◽  
D. M. Turner
Keyword(s):  
Natural Rubber ◽  
Mechanical Behavior ◽  
Material Behavior ◽  
Computationally Efficient ◽  
Complex Deformation ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Basic Equations ◽  
Efficient Approximation ◽  
Natural Rubber Vulcanizates

Abstract Aspects of the mechanical behavior of filled vulcanizates are reviewed with reference to existing mathematical models. The basic equations of the triboelastic theory, previously described by Turner, are derived. A standard triboelastic solid (STS) three parameter model, analogous to the standard linear solid, is described and a computationally efficient approximation developed. Comparisons are made between the predictions of the STS model and the behavior of testpieces of heavily filled natural rubber vulcanizates when subjected to simple and to complex deformation histories at various frequencies; the model is found to give a satisfactory representation of material behavior. Limitations of the STS model are also discussed.

Linear Viscoelastic Creep Model for the Contact of Nominal Flat Surfaces Based on Fractal Geometry: Standard Linear Solid (SLS) Material

2007 ◽  
Vol 129 (3) ◽  
pp. 461-466 ◽  
Author(s):  
Osama M. Abuzeid ◽  
Peter Eberhard
Keyword(s):  
Constitutive Law ◽  
Creep Model ◽  
Viscoelastic Creep ◽  
Flat Surfaces ◽  
Proposed Model ◽  
Linear Viscoelastic ◽  
Standard Linear Solid ◽  
Standard Linear ◽  
Creep Force ◽  
Good Agreement

The objective of this study is to construct a continuous mathematical model that describes the frictionless contact between a nominally flat (rough) viscoelastic punch and a perfectly rigid foundation. The material’s behavior is modeled by assuming a complex viscoelastic constitutive law, the standard linear solid (SLS) law. The model aims at studying the normal compliance (approach) of the punch surface, which will be assumed to be quasistatic, as a function of the applied creep load. The roughness of the punch surface is assumed to be fractal in nature. The Cantor set theory is utilized to model the roughness of the punch surface. An asymptotic power law is obtained, which associates the creep force applied and the approach of the fractal punch surface. This law is only valid if the approach is of the size of the surface roughness. The proposed model admits an analytical solution for the case when the deformation is linear viscoelastic. The modified analytical model shows a good agreement with experimental results available in the literature.

scholarly journals Stable and Efficient Modeling of Anelastic Attenuation in Seismic Wave Propagation

2012 ◽  
Vol 12 (1) ◽  
pp. 193-225 ◽  
Author(s):  
N. Anders Petersson ◽  
Björn Sjögreen
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Half Space ◽  
Material Model ◽  
Second Order ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Space Problem ◽  
Standard Linear Solid ◽  
Standard Linear

AbstractWe develop a stable finite difference approximation of the three-dimensional viscoelastic wave equation. The material model is a super-imposition of N standard linear solid mechanisms, which commonly is used in seismology to model a material with constant quality factor Q. The proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables, making it significantly more memory efficient than the commonly used first order velocity-stress formulation. The new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation [SIAM J. Numer. Anal., 45 (2007), pp. 1902-1936]. Our main result is a proof that the proposed discretization is energy stable, even in the case of variable material properties. The proof relies on the summation-by-parts property of the discretization. The new scheme is implemented with grid refinement with hanging nodes on the interface. Numerical experiments verify the accuracy and stability of the new scheme. Semi-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the accuracy. We find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.

scholarly journals Asymptotic behaviour for the vibrations modeled by the standard linear solid model with a thermal effect

2013 ◽  
Vol 399 (2) ◽  
pp. 472-479 ◽  
Author(s):  
Margareth S. Alves ◽  
Celene Buriol ◽  
Marcio V. Ferreira ◽  
Jaime E. Muñoz Rivera ◽  
Mauricio Sepúlveda ◽  
...  
Keyword(s):  
Asymptotic Behaviour ◽  
Thermal Effect ◽  
Solid Model ◽  
Standard Linear Solid Model ◽  
Standard Linear Solid ◽  
Standard Linear

Effects of hydrophobic treatments of stone on pore water studied by continuous distribution analysis of NMR relaxation times

2001 ◽  
Vol 19 (3-4) ◽  
pp. 509-512 ◽  
Author(s):  
L. Appolonia ◽  
G.C. Borgia ◽  
V. Bortolotti ◽  
R.J.S. Brown ◽  
P. Fantazzini ◽  
...  
Keyword(s):  
Pore Water ◽  
Relaxation Times ◽  
Continuous Distribution ◽  
Nmr Relaxation ◽  
Distribution Analysis ◽  
Nmr Relaxation Times
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