Determination of a Strain Energy Density Function for the Tricuspid Valve Leaflets Using Constant Invariant-Based Mechanical Characterizations

2021 ◽  
Author(s):  
Devin W. Laurence ◽  
Chung-Hao Lee
Keyword(s):  
Energy Density ◽  
Density Function ◽  
Tricuspid Valve ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Confidence Regions ◽  
Exponential Model ◽  
Polynomial Form ◽  
Exponential Form ◽  
Strain Energy Density Function

Abstract The tricuspid valve (TV) regulates the blood flow within the right side of the heart. Despite recent improvements in understanding TV mechanical and microstructural properties, limited attention has been devoted to developments of TV-specific constitutive models. The objective of this work is to use the first-of-its-kind experimental data from constant invariant-based mechanical characterizations to determine a suitable invariant-based strain energy density function (SEDF). Six specimens for each TV leaflet are characterized using constant invariant mechanical testing. The data is then fit with three candidate SEDF forms: (i) a polynomial model as the transversely isotropic version of the Mooney-Rivlin model, (ii) an exponential model, and (iii) a combined polynomial-exponential model. Similar fitting capabilities were found for the exponential and polynomial forms (R2=0.92-0.99 vs. 0.91-0.97) compared to the combined polynomial-exponential SEDF (R2=0.65-0.95). Furthermore, the polynomial form had larger Pearson's correlation coefficients than the exponential form (0.51 vs. 0.30), indicating a more well-defined search space. Finally, the exponential and combined polynomial-exponential forms had notably smaller but more eccentric model parameter's confidence regions than the polynomial form. Further evaluations of invariant decoupling revealed that the decoupling of the invariant terms within the exponential SEDF leads to a less satisfactory performance. From these results, we conclude that the exponential form is better suited for the TV leaflets due to its superb fitting capabilities and smaller parameter's confidence regions.

Large Deformation Analysis of the Arterial Cross Section

1971 ◽  
Vol 93 (2) ◽  
pp. 138-145 ◽  
Author(s):  
B. R. Simon ◽  
A. S. Kobayashi ◽  
D. E. Strandness ◽  
C. A. Wiederhielm
Keyword(s):  
Finite Element ◽  
Energy Density ◽  
Numerical Integration ◽  
Density Function ◽  
Cross Section ◽  
Finite Deformation ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Exponential Form ◽  
Strain Energy Density Function

Possible relations between arterial wall stresses and deformations and mechanisms contributing to atherosclerosis are discussed. Necessary material properties are determined experimentally and from available data in the literature by assuming the arterial response to be a static finite deformation of a thick-walled cylinder constrained in a state of plane strain and composed of an incompressible, nonlinear elastic, transversely isotropic material. Experimental justification from the literature and supporting theoretical considerations are presented for each assumption. The partial derivative of the strain energy density function δW1/δI , necessary for in-plane stress calculation, is determined to be of exponential form using in situ biaxial test results from the canine abdominal aorta. An axisymmetric numerical integration solution is developed and used as a check for finite element results. The large deformation finite element theory of Oden is modified to include aortic material nonlinearity and directional properties and is used for a structural analysis of the aortic cross section. Results of this investigation are: (a) Fung’s exponential form for the strain energy density function of soft tissues is found to be valid for the aorta in the biaxial states considered; (b) finite deformation analyses by the finite element method and numerical integration solution reveal that significant tangential stress gradients are present in arteries commonly assumed to be “thin-walled” tubes using linear theory.

The strain energy density function

1986 ◽  
pp. 237-253
Author(s):  
G. C. Sih ◽  
J. G. Michopoulos ◽  
S. C. Chou
Keyword(s):  
Energy Density ◽  
Density Function ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Strain Energy Density Function

An adaptive meshing automatic scheme based on the strain energy density function

1997 ◽  
Vol 14 (6) ◽  
pp. 604-629 ◽  
Author(s):  
A. Hernández ◽  
J. Albizuri ◽  
M.B.G. Ajuria ◽  
M.V. Hormaza
Keyword(s):  
Energy Density ◽  
Density Function ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Adaptive Meshing ◽  
Strain Energy Density Function

On the Small Strain Behavior of Peroxide Crosslinked Natural Rubber

1986 ◽  
Vol 59 (1) ◽  
pp. 130-137 ◽  
Author(s):  
Gregory B. McKenna ◽  
Louis J. Zapas
Keyword(s):  
Energy Density ◽  
Density Function ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Scaling Law ◽  
Small Strain ◽  
Constant Length ◽  
Strain Behavior ◽  
Small Strains ◽  
Strain Energy Density Function

Abstract Torque and normal force measurements on a cylinder subjected to torsion at constant length were used to study the behavior of NR crosslinked with 5 phr dicumyl peroxide. The derivatives of the strain-energy density function ∂W/∂I1 and ∂W/∂I2 were calculated from the data using the scaling law of Penn and Kearsley. The new results extend the limit of small strains at which the strain-energy density function derivatives have been measured to γ<0.005 and further confirm our previous results that for peroxide-crosslinked NR, ∂W/∂I2 does not become negative at small strain, contrary to several reports in the literature. Reduced stress was determined for the rubber by using the approach of Kearsley and Zapas to calculate the derivative w′(λ) of the Valanis-Landel form of the strain energy function. The results were compared with the measured values for reduced stress in tension and compression at small strains. While the deviation between the predictions and the experimental behavior do not exceed 6%, the characters of the calculated and measured reduced stress plots are different. The measurements in torsion were not obtained at small enough strains to enable direct comparison with the extension/compression behavior at |ε|<0.002. Extrapolation of the results did not produce the anomalous cusp observed in the reduced stress for 0.998<1/λ<1.002 which was reported in our previous study. The fact that torsional data do not show the cusp offers support to the Kearsley suggestion that at these extremely small deformations, rubber compressibility may play an important role in the stress-strain behavior. This could also explain the apparent discrepancy between the predicted Valanis-Landel behavior and the observed behavior. Future work involving higher precision experiments is required to resolve the matter.

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