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

2008 ◽  
Vol 130 (6) ◽  
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.

Stress integration procedures for inelastic material models within the Finite Element Method

2002 ◽  
Vol 55 (4) ◽  
pp. 389-414 ◽  
Author(s):  
Milosˇ Kojic´
Keyword(s):  
Finite Element ◽  
Large Strain ◽  
Deformation Gradient ◽  
Design And Technology ◽  
Parameter Method ◽  
Material Models ◽  
Mapping Procedure ◽  
Inelastic Material ◽  
Tangent Moduli ◽  
Stress Integration

A review of numerical procedures for stress calculation in the inelastic finite element analysis is presented. The role of stress integration within a time (load) step in the incremental-iterative scheme for the displacements based FE formulation is first given briefly. Then, the basic relations of the explicit algorithms, as the first ones developed in the 70s, are presented. The shortcomings of these algorithms are pointed out. The implicit procedures are presented in some detail, with the emphasis on a general return mapping procedure and the governing parameter method (GPM). Derivation of the consistent tangent moduli represents an important task in the inelastic FE analysis because the overall equilibrium iteration rate depends on these moduli. The basic concepts of this derivation are presented. An important field, very challenging in today’s stage of design and technology, is the large strain deformation of material. A review of the approaches in the large strain domain that includes the rate and the total formulations is given in some detail. Special attention is devoted to the multiplicative decomposition of deformation gradient concept, since that concept is generally favored today. Some unresolved issues, such as the use of the stress and strain measures, are discussed briefly. A number of selected numerical examples illustrate the main topics in the stress integration task, as well as the applications of the stress integration algorithms to various material models. Some concluding remarks and an outline of further research topics are given at the end of the paper. This review article includes 205 references.

Development of Material Constants for Nonlinear Finite-Element Analysis

1988 ◽  
Vol 61 (5) ◽  
pp. 879-891 ◽  
Author(s):  
Robert H. Finney ◽  
Alok Kumar
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Large Strain ◽  
Strain Range ◽  
Nonlinear Finite Element ◽  
Element Analysis ◽  
Material Models ◽  
Tensile Data

Abstract The determination of the material coefficients for Ogden, Mooney-Rivlin, Peng, and Peng-Landel material models using simple ASTM D 412 tensile data is shown to be a manageable task. The application of the various material models are shown to be subject to the type and level of deformation expected, with Ogden showing the best correlation with experimental data over a large strain range for the three types of strain investigated. At low strains, all of the models showed reasonable correlation.

Hexahedral-Based Smoothed Finite Element Method Using Volumetric-Deviatoric Split for Contact Problem

2018 ◽  
Vol 940 ◽  
pp. 84-88 ◽  
Author(s):  
Kai Oshiro ◽  
Hiroka Miyakubo ◽  
Masaki Fujikawa ◽  
Chobin Makabe
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Contact Problem ◽  
Large Strain ◽  
Deformation Gradient ◽  
Deformation Analysis ◽  
Tetrahedral Elements ◽  
Incompressible Materials ◽  
Smoothed Finite Element Method ◽  
Element Method

A first-order hexahedral (H8)-element-based smoothed finite element method (S-FEM) with a volumetric-deviatoric split for nearly incompressible materials was developed for highly accurate deformation analysis of large-strain problems. In the proposed method, the isovolumetric part of the deformation gradient at the integration point is derived from F based on the beta finite element method (i.e., an S-FEM), whereas the volumetric part of the deformation gradient is derived from F on the basis of the standard FEM with reduced integration elements. This method targets H8 elements that are automatically generated from tetrahedral elements, which makes it quite practical. This is because the FE mesh can be created automatically even if the targeted object has a complex shape. This method eliminates the phenomena of volumetric and shear locking, and reduces pressure oscillations. The proposed method was implemented in the commercial FE software Abaqus and applied to the large-deformation contact problem to verify its effectiveness.

scholarly journals New Analytical Model for Swellable Materials

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.

scholarly journals 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 ◽  
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.

scholarly journals Numerical Approximation of Elasticity Tensor Associated With Green-Naghdi Rate

2017 ◽  
Vol 139 (8) ◽  
Author(s):  
Haofei Liu ◽  
Wei Sun
Keyword(s):  
Finite Element ◽  
Approximation Method ◽  
Numerical Approximation ◽  
Evaluation Process ◽  
Elasticity Tensor ◽  
Fe Analysis ◽  
Tangent Modulus ◽  
Material Models ◽  
Complex Material ◽  
Objective Stress

Objective stress rates are often used in commercial finite element (FE) programs. However, deriving a consistent tangent modulus tensor (also known as elasticity tensor or material Jacobian) associated with the objective stress rates is challenging when complex material models are utilized. In this paper, an approximation method for the tangent modulus tensor associated with the Green-Naghdi rate of the Kirchhoff stress is employed to simplify the evaluation process. The effectiveness of the approach is demonstrated through the implementation of two user-defined fiber-reinforced hyperelastic material models. Comparisons between the approximation method and the closed-form analytical method demonstrate that the former can simplify the material Jacobian evaluation with satisfactory accuracy while retaining its computational efficiency. Moreover, since the approximation method is independent of material models, it can facilitate the implementation of complex material models in FE analysis using shell/membrane elements in abaqus.

Finite Element Analysis for Normal-Temperature Wet Briquetting of Straws

2012 ◽  
Vol 512-515 ◽  
pp. 409-415
Author(s):  
Jian Jun Hu ◽  
Ting Zhou Lei ◽  
Sheng Qiang Shen ◽  
Quan Guo Zhang
Keyword(s):  
Finite Element ◽  
Fossil Fuels ◽  
Large Strain ◽  
Body Movement ◽  
Deformation Gradient ◽  
Computer Software ◽  
Practical Significance ◽  
Gradient Tensor ◽  
Element Analysis ◽  
Balance Principle

As one of important technologies for briquettes production from straws, the normal-temperature wet briquetting technology of straws shows important practical significance in place of fossil fuels that are progressively reduced. According to the characteristics of the normal-temperature wet briquetting of straws having large displacement and large strain, this article provided a finite element calculation method for non-linear straw problems using the large-deformation elastic-plasticity principle. Based on description of straw status by Lagrange method, analyses were performed for deformation gradient tensor, displacement gradient tensor and rigid body movement, and then finite element equations were established for the normal-temperature wet briquetting of straws according to the Green strain, Drucker-Prager criterion and balance principle, providing references for numerical simulation for the normal-temperature wet briquetting of straws with computer software.

Use of the Finite Element Analysis Method in Pedodontics

2018 ◽  
Vol 55 (4) ◽  
pp. 666-675
Author(s):  
Mihaela Tanase ◽  
Dan Florin Nitoi ◽  
Marina Melescanu Imre ◽  
Dorin Ionescu ◽  
Laura Raducu ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Structural Model ◽  
Analysis Method ◽  
Ansys Software ◽  
Concentrated Force ◽  
Element Analysis ◽  
Finite Element Analysis Method ◽  
The Finite Element Analysis ◽  
Solid Type

The purpose of this study was to determinate , using the Finite Element Analysis Method, the mechanical stress in a solid body , temporary molar restored with the self-curing GC material. The originality of our study consisted in using an accurate structural model and applying a concentrated force and a uniformly distributed pressure. Molar structure was meshed in a Solid Type 45 and the output data were obtained using the ANSYS software. The practical predictions can be made about the behavior of different restorations materials.

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