A novel phenomenological viewpoint for transversely isotropic hyperelastic materials; a new 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.

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The Effect of Mixing Method on the Strain Energy Density Function of Carbon Black Reinforced Rubber

NIPPON GOMU KYOKAISHI ◽

10.2324/gomu.73.653 ◽

2000 ◽

Vol 73 (12) ◽

pp. 653-659

Author(s):

Yoshihiro YAMASHITA ◽

Sueo KAWABATA

Keyword(s):

Energy Density ◽

Carbon Black ◽

Density Function ◽

Strain Energy Density ◽

Strain Energy ◽

Strain Energy Density Function ◽

Mixing Method

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Development of Hyperelastic Model for Weldlines Containing Natural Rubber Molded Part

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.747.631 ◽

2013 ◽

Vol 747 ◽

pp. 631-634

Author(s):

Watcharapong Chookaew ◽

Jirachai Mingbunjurdsuk ◽

Pairote Jittham ◽

Somjate Patcharaphun

Keyword(s):

Energy Density ◽

Strain Energy Density ◽

Strain Energy ◽

Mathematical Formulation ◽

Constitutive Models ◽

Hyperelastic Materials ◽

Design Engineers ◽

Strain Energy Density Function ◽

Molded Part ◽

Rubber Part

Several constitutive models of non-linear large elastic deformation based on strain-energy-density functions have been developed for hyperelastic materials. These models, coupled with the Finite Element Method (FEM), can effectively utilized by design engineers to analyze and design elastomeric products operating under the deformation states. However, due to the complexities of the mathematical formulation which can only obtained at the moderate strain and the assumption of material used for the analysis. Therefore it is formidable task for design engineer to make use of these constitutive relationships. In the present work, the strain-energy-density function of weldline containing rubber part was constructed by using the Neural Network (NN) model. The analytical results were compared to those obtained by Neo-Hookean, Mooney-Rivlin, Ogden models. Good agreement between developed NN model and the existing experimental data was found, especially at very low strain and at very high strain.

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