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 On the Design of a Biodegradable POC-HA Polymeric Cardiovascular Stent

2012 ◽  
Author(s):  
Joonas Ponkala ◽  
Mohsin Rizwan ◽  
Panos S. Shiakolas
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Material Properties ◽  
Three Dimensional ◽  
Polymeric Composite ◽  
Coronary Stent ◽  
Element Analysis ◽  
Material Models ◽  
Solid Models ◽  
Biodegradable Stents

The current state of the art in coronary stent technology, tubular structures used to keep the lumen open, is mainly populated by metallic stents coated with certain drugs to increase biocompatibility, even though experimental biodegradable stents have appeared in the horizon. Biodegradable polymeric stent design necessitates accurate characterization of time dependent polymer material properties and mechanical behavior for analysis and optimization. This manuscript presents the process for evaluating material properties for biodegradable biocompatible polymeric composite poly(diol citrate) hydroxyapatite (POC-HA), approaches for identifying material models and three dimensional solid models for finite element analysis and fabrication of a stent. The developed material models were utilized in a nonlinear finite element analysis to evaluate the suitability of the POC-HA material for coronary stent application. In addition, the advantages of using femtosecond laser machining to fabricate the POC-HA stent are discussed showing a machined stent. The methodology presented with additional steps can be applied in the development of a biocompatible and biodegradable polymeric stents.

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.

scholarly journals Benchmark for the Coupled Magneto-Mechanical Boundary Value Problem in Magneto-Active Elastomers

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2380
Author(s):  
Philipp Metsch ◽  
Raphael Schiedung ◽  
Ingo Steinbach ◽  
Markus Kästner
Keyword(s):  
Finite Element ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Three Dimensional ◽  
Diffuse Interface ◽  
Two Dimensional ◽  
Benchmark Problem ◽  
Material Models ◽  
Lagrangian Finite Element ◽  
Good Agreement

Within this contribution, a novel benchmark problem for the coupled magneto-mechanical boundary value problem in magneto-active elastomers is presented. Being derived from an experimental analysis of magnetically induced interactions in these materials, the problem under investigation allows us to validate different modeling strategies by means of a simple setup with only a few influencing factors. Here, results of a sharp-interface Lagrangian finite element framework and a diffuse-interface Eulerian approach based on the application of a spectral solver on a fixed grid are compared for the simplified two-dimensional as well as the general three-dimensional case. After influences of different boundary conditions and the sample size are analyzed, the results of both strategies are examined: for the material models under consideration, a good agreement of them is found, while all discrepancies can be ascribed to well-known effects described in the literature. Thus, the benchmark problem can be seen as a basis for future comparisons with both other modeling strategies and more elaborate material models.

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.

Structural Analysis

2017 ◽  
pp. 124-219
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Analysis ◽  
Numerical Methods ◽  
Three Dimensional ◽  
Wind Engineering ◽  
The Finite Element Method ◽  
Material Models ◽  
Three Dimensional Models ◽  
Base Connections

This chapter develops the components required for successful modelling of temporary structures. It presents the principles, methods and the associated limitations that currently are seen as the state-of-the-art in structural analysis using the Finite Element Method. Material models of steel, aluminium and bamboo are presented with an emphasis on linear and multilinear models for steel and the Ramberg-Osgood model for aluminium. Models are presented for braces, props, beam-to-column connections, top connections, base connections and column-to-column connections based on the latest theoretical and experimental procedures developed by the authors and co-workers. Examples of two and three dimensional models are then developed for access scaffolds, bridge falsework and bamboo scaffolds. Finally, the chapter presents information on the effects of ground modelling and on advanced wind engineering using complex numerical methods.

Use of General Nonlinear Material Models in Beam Problems: Application to Belts and Rubber Chains

2010 ◽  
Vol 5 (2) ◽  
Author(s):  
Luis G. Maqueda ◽  
Abdel-Nasser A. Mohamed ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Large Deformation ◽  
Cross Section ◽  
Multibody System ◽  
Three Dimensional ◽  
Nonlinear Material ◽  
Tracked Vehicle ◽  
Material Models ◽  
Belt Drives ◽  
Linear And Nonlinear

Accurate modeling of many engineering systems requires the integration of multibody system and large deformation finite element algorithms that are based on general constitutive models, account for the coupling between the large rotation and deformation, and allow capturing coupled deformation modes that cannot be captured using beam formulations implemented in existing computational algorithms and computer codes. In this investigation, new three-dimensional nonlinear dynamic rubber chains and belt drives models are developed using the finite element absolute nodal coordinate formulation (ANCF) that allows for a straight forward implementation of general linear and nonlinear material models for structural elements such as beams, plates, and shells. Furthermore, this formulation, which is based on a more general kinematic description, can be used to predict the cross section deformation and its coupling with the extension and bending of the belt drives and rubber chains. The ANCF cross section deformation results are validated by comparison with the results obtained using solid finite elements in the case of a simple tension test problem. The effect of the use of different linear and nonlinear constitutive laws in modeling belt drive mechanisms is also examined in this investigation. The finite element formulation presented in this paper is implemented in a general purpose three-dimensional flexible multibody algorithm that allows for developing detailed models of mechanical systems subject to general loading conditions, nonlinear algebraic constraint equations, and arbitrary large displacements that characterize belt drives and tracked vehicle dynamics. The successful integration of large deformation finite element and multibody system algorithms is shown to be necessary in order to be able to study the dynamics of complex tracked vehicles with rubber chains. A computer simulation of a three-dimensional multibody tracked vehicle model that consists of twenty rigid bodies and two flexible rubber chains is used in order to demonstrate the use of the formulations presented in this investigation.

Use of General Nonlinear Material Models in Beam Problems: Application to Belt and Rubber Chains

2009 ◽  
Author(s):  
Luis G. Maqueda ◽  
Abdel-Nasser A. Mohamed ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Large Deformation ◽  
Cross Section ◽  
Multibody System ◽  
Three Dimensional ◽  
Nonlinear Material ◽  
Tracked Vehicle ◽  
Material Models ◽  
Belt Drives ◽  
Linear And Nonlinear

Accurate modeling of many engineering systems requires the integration of multibody system and large deformation finite element algorithms that are based on general constitutive models, account for the coupling between the large rotation and deformation, and allow capturing coupled deformation modes that cannot be captured using beam formulations implemented in existing computational algorithms and computer codes. In this investigation, a new nonlinear finite element dynamic model for the analysis of three-dimensional rubber chains and belt drives is developed using the finite element absolute nodal coordinate formulation (ANCF) that allows for a straight forward implementation of general linear and nonlinear material models for structural elements such as beams, plates and shells. Furthermore, this formulation, which is based on a more general kinematic description, can be used to predict the cross section deformation and its coupling with the extension and bending of the belt drives and rubber chains. The ANCF cross section deformation results are validated by comparison with the results obtained using solid finite elements in the case of a simple tension test problem. The effect of the use of different linear and nonlinear constitutive laws in modeling belt drives mechanism is also examined in this investigation. The finite element formulation presented in this paper is implemented in a general purpose three-dimensional flexible multibody algorithm that allows for developing detailed models of mechanical systems subject to general loading conditions, nonlinear algebraic constraint equations, and arbitrary large displacements that characterize belt drives and tracked vehicle dynamics. The successful integration of large deformation finite element and multibody system algorithms is shown to be necessary in order to be able to study the dynamics of complex tracked vehicles with rubber chains. A computer simulation of a three-dimensional multibody tracked vehicle model that consists of twenty rigid bodies and two flexible rubber chains is used in order to demonstrate the use of the formulations presented in this investigation.

COMPARATIVE STUDY ON STRENGTH OF KNEE JOINT USING VARIOUS MATERIAL MODELS

2012 ◽  
Vol 01 (02) ◽  
pp. 1250013 ◽  
Author(s):  
ZHENGZHI YANG ◽  
ZHIWEI DING ◽  
ZISHUN LIU ◽  
SOMSAK SWADDIWUDHIPONG ◽  
YI MIN TAN ◽  
...  
Keyword(s):  
Finite Element ◽  
Knee Joint ◽  
Comparative Study ◽  
Material Properties ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Element Model ◽  
Material Models ◽  
Vertical Loading ◽  
Human Knee Joint

In this study, we adopt different material models to study the strength and stiffness of menisci of the knee joint using finite element method. The three-dimensional (3-D) knee joint finite element model is constructed based on the Magnetic Resonance (MR) images of a human knee joint, and the strength of menisci is analyzed under a specific vertical loading case. In this paper we categorize and implement three types of appropriate material properties, namely isotropic linearly elastic, transversely isotropic elastic and isotropic hyperelastic for menisci of the knee joint. Different strain energy models are also studied and compared under hyperelastic category. The comparative study demonstrates that the hyperelastic model with Ogden form is more appropriate in modeling menisci of the knee joint. By referring to the test data of different material properties from earlier studies by various researchers, we hope to provide a comparative study leading to appropriate menisci material models and properties for finite element analyses of knee joint structures.

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