The Use of Hyperelastic Material Models for Estimation of Pig Aorta Biomechanical Behavior

This paper presents a mode-based elastohydrodynamic formulation employing low-modulus hyperelastic material models which exhibit strongly non-linear load-deflection characteristics. The mode-based method is applied to a reciprocating liquid O-ring seal, where it is found under steady axial motion that a relatively small set of modes captures the essential features of seal deformation when compared with that obtained with standard node-based methods.

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A general framework for the numerical implementation of anisotropic hyperelastic material models including non-local damage

Biomechanics and Modeling in Mechanobiology ◽

10.1007/s10237-017-0875-9 ◽

2017 ◽

Vol 16 (4) ◽

pp. 1119-1140 ◽

Cited By ~ 8

Author(s):

J. P. S. Ferreira ◽

M. P. L. Parente ◽

M. Jabareen ◽

R. M. Natal Jorge

Keyword(s):

General Framework ◽

Hyperelastic Material ◽

Local Damage ◽

Numerical Implementation ◽

Material Models ◽

Non Local

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Numerical Approximation of Tangent Moduli for Finite Element Implementations of Nonlinear Hyperelastic Material Models

Journal of Biomechanical Engineering ◽

10.1115/1.2979872 ◽

2008 ◽

Vol 130 (6) ◽

Cited By ~ 54

Author(s):

Wei Sun ◽

Elliot L. Chaikof ◽

Marc E. Levenston

Keyword(s):

Finite Element ◽

Numerical Approximation ◽

Structural Model ◽

Large Strain ◽

Deformation Gradient ◽

Mathematical Formulation ◽

Hyperelastic Material ◽

Material Models ◽

Tangent Stiffness Matrix ◽

Tangent Moduli

Finite element (FE) implementations of nearly incompressible material models often employ decoupled numerical treatments of the dilatational and deviatoric parts of the deformation gradient. This treatment allows the dilatational stiffness to be handled separately to alleviate ill conditioning of the tangent stiffness matrix. However, this can lead to complex formulations of the material tangent moduli that can be difficult to implement or may require custom FE codes, thus limiting their general use. Here we present an approach, based on work by Miehe (Miehe, 1996, “Numerical Computation of Algorithmic (Consistent) Tangent Moduli in Large Strain Computational Inelasticity,” Comput. Methods Appl. Mech. Eng., 134, pp. 223–240), for an efficient numerical approximation of the tangent moduli that can be easily implemented within commercial FE codes. By perturbing the deformation gradient, the material tangent moduli from the Jaumann rate of the Kirchhoff stress are accurately approximated by a forward difference of the associated Kirchhoff stresses. The merit of this approach is that it produces a concise mathematical formulation that is not dependent on any particular material model. Consequently, once the approximation method is coded in a subroutine, it can be used for other hyperelastic material models with no modification. The implementation and accuracy of this approach is first demonstrated with a simple neo-Hookean material. Subsequently, a fiber-reinforced structural model is applied to analyze the pressure-diameter curve during blood vessel inflation. Implementation of this approach will facilitate the incorporation of novel hyperelastic material models for a soft tissue behavior into commercial FE software.

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New Analytical Model for Swellable Materials

10.5772/intechopen.94732 ◽

2021 ◽

Author(s):

Sayyad Zahid Qamar ◽

Maaz Akhtar ◽

Tasneem Pervez

Keyword(s):

Finite Element ◽

Three Dimensional ◽

Hyperelastic Material ◽

Behavior Patterns ◽

Material Models ◽

Maximum Resistance ◽

New Models ◽

Major Shortcoming ◽

Gaussian Statistics ◽

Solvent Molecules

As discussed in Chapter 6, numerical prediction of swelling can be attempted using existing hyperelastic material models available in commercial finite element (FE) packages. However, none of these models can accurately represent the behavior of swelling elastomers. The major shortcoming of currently available swelling models is that they consider Gaussian statistics for mechanical contribution of configuration entropy, which is based on chains having limited extensibility. Some later models (not yet incorporated into commercial FE packages) can give a reasonable account of certain behavior patterns in swelling elastomers, but do not explain other aspects well. One of the new approaches is to treat swelling elastomers as gels. As described earlier, gels are mostly liquid, yet they behave like solids due to a three-dimensional cross-linked network within the liquid. Many authors consider gel as poro-elastic or porous and use Darcy’s law to model the amount of fluid influx. However, a swollen elastomer mostly consists of the solvent. When an external load is applied, maximum resistance comes from the solvent molecules as in diffusion. Also, most of the new models are quite complex in concept and formulation, and there is a serious need for a scientifically simpler model.

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The Uniaxial Stress–Strain Relationship of Hyperelastic Material Models of Rubber Cracks in the Platens of Papermaking Machines Based on Nonlinear Strain and Stress Measurements with the Finite Element Method

Materials ◽

10.3390/ma14247534 ◽

2021 ◽

Vol 14 (24) ◽

pp. 7534

Author(s):

Huu-Dien Nguyen ◽

Shyh-Chour Huang

Keyword(s):

Finite Element ◽

Working Conditions ◽

Uniaxial Stress ◽

Hyperelastic Material ◽

The Finite Element Method ◽

Stress Strain ◽

Material Models ◽

Strain Relationship ◽

Relationship Of ◽

Better Than

Finite element analysis is extensively used in the design of rubber products. Rubber products can suffer from large amounts of distortion under working conditions as they are nonlinearly elastic, isotropic, and incompressible materials. Working conditions can vary over a large distortion range, and relate directly to different distortion modes. Hyperelastic material models can describe the observed material behaviour. The goal of this investigation was to understand the stress and relegation fields around the tips of cracks in nearly incompressible, isotropic, hyperelastic accouterments, to directly reveal the uniaxial stress–strain relationship of hyperelastic soft accouterments. Numerical and factual trials showed that measurements of the stress–strain relationship could duly estimate values of nonlinear strain and stress for the neo-Hookean, Yeoh, and Arruda–Boyce hyperelastic material models. Numerical models were constructed using the finite element method. It was found that results concerning strains of 0–20% yielded curvatures that were nearly identical for both the neo-Hookean, and Arruda–Boyce models. We could also see that from the beginning of the test (0–5% strain), the curves produced from our experimental results, alongside those of the neo-Hookean and Arruda–Boyce models were identical. However, the experiment’s curves, alongside those of the Yeoh model, converged at a certain point (30% strain for Pieces No. 1 and 2, and 32% for Piece No. 3). The results showed that these finite element simulations were qualitatively in agreement with the actual experiments. We could also see that the Yeoh models performed better than the neo-Hookean model, and that the neo-Hookean model performed better than the Arruda–Boyce model.

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