New experiments on shear modulus of elasticity of arteries

1994 ◽  
Vol 266 (1) ◽  
pp. H1-H10 ◽  
Author(s):  
S. X. Deng ◽  
J. Tomioka ◽  
J. C. Debes ◽  
Y. C. Fung
Keyword(s):  
Blood Pressure ◽  
Shear Modulus ◽  
Modulus Of Elasticity ◽  
Vessel Wall ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
New Instrument ◽  
Rat Thoracic Aorta ◽  
The Difference

Although the mechanical properties of blood vessels have been studied extensively, the shear modulus of the blood vessel wall is still unknown. New data on the shear modulus of elasticity of rat arteries and its variation with axial stretch and blood pressure are presented. The data were obtained from a new instrument designed and constructed by us to perform simultaneous torsion, inflation, and longitudinal stretching tests. It was found under physiological conditions (pressure = 120 mmHg or 16 kPa; longitudinal stretch = 1.2 relative to zero-stress state), the shear modulus of normal rat thoracic aorta is G = 137 +/- 18 kPa. The difference of shear modulus at body temperature (37 degrees C) and room temperature (25 degrees C) is within 10%. The shear modulus varies significantly with changing longitudinal and circumferential strains in proportion to the strain energy due to these strains. A constitutive equation based on a pseudo strain energy function is proposed. The vessel wall is not transversely isotropic in the incremental sense. When the rat was subjected to high blood pressure due to constriction of its aorta, the shear modulus does not vary significantly with the length of time the animal was subjected to hypertension.

Three-Dimensional Stress Distribution in Arteries

1983 ◽  
Vol 105 (3) ◽  
pp. 268-274 ◽  
Author(s):  
C. J. Chuong ◽  
Y. C. Fung
Keyword(s):  
Experimental Data ◽  
Stress Distribution ◽  
Vessel Wall ◽  
Strain Energy ◽  
Arterial Wall ◽  
Three Dimensional ◽  
Strain Energy Function ◽  
Exponential Form ◽  
Strain Relationship ◽  
Longitudinal Stretch

A three-dimensional stress-strain relationship derived from a strain energy function of the exponential form is proposed for the arterial wall. The material constants are identified from experimental data on rabbit arteries subjected to inflation and longitudinal stretch in the physiological range. The objectives are: 1) to show that such a procedure is feasible and practical, and 2) to call attention to the very large variations in stresses and strains across the vessel wall under the assumptions that the tissue is incompressible and stress-free when all external load is removed.

A Simple Transversely Isotropic Hyperelastic Constitutive Model Suitable for Finite Element Analysis of Fiber Reinforced Elastomers

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Leslee W. Brown ◽  
Lorenzo M. Smith
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Material Model ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
Material Tests

A transversely isotropic fiber reinforced elastomer’s hyperelasticity is characterized using a series of constitutive tests (uniaxial tension, uniaxial compression, simple shear, and constrained compression test). A suitable transversely isotropic hyperelastic invariant based strain energy function is proposed and methods for determining the material coefficients are shown. This material model is implemented in a finite element analysis by creating a user subroutine for a commercial finite element code and then used to analyze the material tests. A useful set of constitutive material data for multiple modes of deformation is given. The proposed strain energy function fits the experimental data reasonably well over the strain region of interest. Finite element analysis of the material tests reveals further insight into the materials constitutive nature. The proposed strain energy function is suitable for finite element use by the practicing engineer for small to moderate strains. The necessary material coefficients can be determined from a few simple laboratory tests.

On the Constitutive Equations of Biological Materials

1975 ◽  
Vol 42 (1) ◽  
pp. 242-243 ◽  
Author(s):  
H. Demiray
Keyword(s):  
Energy Function ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Biological Materials ◽  
Biological Tissues

This paper deals with a simple possible form of the strain-energy function for biological tissues which are assumed to be transversely isotropic. Also the solution of a problem is studied and the result is compared with experiments.

MECHANICAL BEHAVIOUR OF TRANSVERSELY ISOTROPIC POROUS NEO-HOOKEAN SOLIDS

2010 ◽  
Vol 02 (01) ◽  
pp. 11-39 ◽  
Author(s):  
ZAOYANG GUO ◽  
FERHUN C. CANER
Keyword(s):  
Strain Energy ◽  
Hydrostatic Stress ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Axial Direction ◽  
Shear Loading ◽  
Porous Solid ◽  
Mechanical Responses ◽  
Cylindrical Pores ◽  
Hyperelastic Model

In this paper, the mechanical responses of a recently developed hyperelastic model for the neo-Hookean solids with aligned continuous cylindrical pores under finite homogeneous deformation that can capture the anisotropic compressibility as well as the coupling between the volumetric and deviatoric behaviours are examined. To this end, the strain energy function of this hyperelastic compressible transversely isotropic model contains terms for the coupling of volumetric and deviatoric behaviours. It is shown that, the asymptotic response of this anisotropic compressible model under extreme loading situations is considerably different from that of incompressible models. The unstable behaviour of the porous solid under hydrostatic stress/strain loadings is discussed in detail. When a general simple 2D shear deformation is applied to this porous solid in i1 – i2 plane, the normal stress in the third axial direction (i3) is nonzero. The loss of monotonicity of the stress tensor under off-axis simple 2D shear loading is demonstrated as well.

A Structural Strain Energy Function for Vascular Tissue Considering Elastin Anisotropy

2007 ◽  
Author(s):  
Rana Rezakhaniha ◽  
Nikos Stergiopulos
Keyword(s):  
Energy Function ◽  
Constitutive Equations ◽  
Vessel Wall ◽  
Strain Energy ◽  
Vascular Tissue ◽  
Strain Energy Function ◽  
Nonlinear Properties ◽  
Wide Range ◽  
Nonlinear Elastic ◽  
Structural Strain

The vessel wall exhibits relatively strong nonlinear properties and undergoes a wide range of deformations. Identification of a strain energy function (SEF) is the preferred method to describe the complex nonlinear elastic properties of the vascular tissue. Once the strain energy function is known, constitutive equations can be obtained.

Characterization of Elastic Properties of Carbon-Black-Filled Rubber Vulcanizates

1990 ◽  
Vol 63 (5) ◽  
pp. 792-805 ◽  
Author(s):  
O. H. Yeoh
Keyword(s):  
Carbon Black ◽  
Shear Modulus ◽  
Elastic Properties ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Stress Strain ◽  
Filled Rubber ◽  
Filled Rubbers

Abstract A novel strain-energy function which is a simple cubic equation in the invariant (I1−3) is proposed for the characterization of the elastic properties of carbon-black-filled rubber vulcanizates. Conceptually, the proposed function is a material model with a shear modulus which varies with deformation. This contrasts with the neo-Hookean and Mooney-Rivlin models which have a constant shear modulus. The variation of shear modulus with deformation is commonly observed with filled rubbers. Initially, the modulus falls with increasing deformation, leading to a flattening of the shear stress/strain curve. At large deformations, the modulus rises again due to finite extensibility of the network, accentuated by the strain amplication effect of the filler. This characteristic behavior of filled rubbers may be described approximately by the proposed strain-energy function by requiring the coefficient C20 to be negative, while the coefficients C10 and C30 are positive. The use of the proposed strain-energy function has been shown to permit the prediction of stress/strain behavior in different deformation modes from data obtained in one simple deformation mode. This circumvents the need for a rather difficult experiment in general biaxial extension. The simple form of the proposed function also simplifies the regression analysis. This strain-energy function is consistent with the general Rivlin strain-energy function and is easily obtained from the popular third-order deformation approximation. Thus, it is already available in many existing finite-element analysis programs.

Patient-Specific Aneurysms Rupture Prediction Using CFD Modelling With Strain Energy Function

2013 ◽  
Author(s):  
A. H. Embong ◽  
A. M. Al-Jumaily ◽  
Giri Mahadevan ◽  
Shukei Sugita ◽  
Andrew Lowe
Keyword(s):  
Vessel Wall ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Wall Stress ◽  
Aneurysm Rupture ◽  
Patient Specific ◽  
Cfd Model ◽  
Cfd Modelling ◽  
Strain Relationship ◽  
Strain Function

This paper proposes a new Patient-Specific Aneurysm CFD Model (PSAM) which is based on the energy strain function combined with dilated vessel wall stress-strain relationship to predict aneurysm rupture. The PSAM relies on the available mechanical properties and parameters obtained from a personalized model. A personalized model is developed based on instantaneous arterial deformations obtained from Doppler Ultrasound (US) images at 6–9 MHz. It is shown that PSAM has the ability to correlate the deformation wall energy based on continuous patient-specifics in predicting rupture.

Orientation Effects in Short Fibre-Reinforced Elastomers

2014 ◽  
Author(s):  
Jacopo Ciambella ◽  
David C. Stanier
Keyword(s):  
Strain Energy ◽  
Large Strain ◽  
Strain Energy Function ◽  
Transversely Isotropic ◽  
Short Fibre ◽  
Rubber Matrix ◽  
Carbon Fibres ◽  
Reinforced Composite ◽  
Strain Behaviour ◽  
Short Carbon

The large strain behaviour of a short fibre-reinforced composite is studied through numerical simulations. The reinforcing fibres yield the macroscopic response transversely isotropic which is indeed the case of many reinforcements currently used in composites: short carbon fibres, cellulose whiskers, carbon nanotubes. As a result of the analysis, it is shown that the reorientation of the fibres that takes place at large strain has a significant effect on the overall material response by changing the axis of isotropy. This behaviour can be adequately described by using a transversely isotropic model whose strain energy function depends on three invariants: two isotropic and one representing the stretch along the direction of the fibres. To assess its capabilities, the model is compared to the results of experiments carried out by the authors on nickel-coated chopped carbon fibres in a vulcanised natural rubber matrix for which the fibre orientation is achieved by controlling an external magnetic field prior to curing. Possible applications include micro-sized propulsion devices and actuators.

The Shear Modulus of Liquid Foam

1984 ◽  
Vol 51 (2) ◽  
pp. 229-231 ◽  
Author(s):  
D. Stamenovic ◽  
T. A. Wilson
Keyword(s):  
Surface Tension ◽  
Shear Modulus ◽  
Energy Function ◽  
Strain Energy ◽  
Strain Energy Function ◽  
Volume Ratio ◽  
Total Surface Area ◽  
Elastic Response ◽  
The Mean ◽  
Liquid Foam

A strain energy function for liquid foam is formulated by modeling foam as a collection of randomly oriented surfaces with surface tension on the faces. The surfaces are assumed to follow the mean strain. It is assumed that surface forces equilibriate between neighboring elements and hence that the value of surface tension γ is the same on all faces and a function of total surface area. In particular, an expansion of the strain energy function in powers of the strain is used to obtain the value for the shear modulus in the linear elasticity approximation. The predicted value of the shear modulus is 4/15 γS/ V where S/ V is the surface to volume ratio or 2/5 ΔP, where ΔP is the overpressure of the gas trapped in the foam. In rheometric tests, foam was found to behave as a viscoelastic material. The shear modulus that describes the initial elastic response was found to be about 84 percent of the predicted value.

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