Development of Constitutive Models for Poro-Hyperelastic Materials

2020 ◽  
pp. 95-177
Author(s):  
Michael Drass
Keyword(s):  
Constitutive Models ◽  
Hyperelastic Materials

Implementing Stretch-Based Strain Energy Functions in Large Coupled Axial and Torsional Deformations of Functionally Graded Cylinder

2019 ◽  
Vol 11 (04) ◽  
pp. 1950039 ◽  
Author(s):  
Arash Valiollahi ◽  
Mohammad Shojaeifard ◽  
Mostafa Baghani
Keyword(s):  
Finite Element ◽  
Hoop Stress ◽  
Constitutive Models ◽  
Elastic Solid ◽  
Functionally Graded ◽  
Deformation Tensor ◽  
Element Analysis ◽  
Hyperelastic Materials ◽  
Ogden Model ◽  
Exponential Power

In this paper, coupled axial and torsional large deformation of an incompressible isotropic functionally graded nonlinearly elastic solid cylinder is investigated. Utilizing stretch-based constitutive models, where the deformation tensor is non-diagonal is complex. Hence, an analytical approach is presented for combined extension and torsion of functionally graded hyperelastic cylinder. Also, finite element analysis is carried out to verify the proposed analytical solutions. The Ogden model is employed to predict the mechanical behavior of hyperelastic materials whose material parameters are function of radius in an exponential fashion. Both finite element and analytical results are in good agreement and reveal that for positive values of exponential power in material variation function, stress decreases and the rate of stress variation intensifies near the outer surface. A transition point for the hoop stress is identified, where the distribution plots regardless of the value of stretch or twist, intersect and the hoop stress alters from compressive to tensile. For the Ogden model, the torsion induced force is always compressive which means the total axial force starts from being tensile and then eventually becomes compressive i.e., the cylinder always tends to elongate on twisting.

Development of Hyperelastic Model for Weldlines Containing Natural Rubber Molded Part

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.

A Finite Element Implementation of Knowles Stored-Energy Function: Theory, Coding and Applications

2011 ◽  
Vol 58 (3) ◽  
pp. 319-346 ◽  
Author(s):  
Cyprian Suchocki
Keyword(s):  
Finite Element ◽  
Energy Function ◽  
Function Theory ◽  
Constitutive Models ◽  
Elasticity Tensor ◽  
Stored Energy ◽  
Energy Potential ◽  
Hyperelastic Materials ◽  
Finite Element Implementation ◽  
Living Tissues

A Finite Element Implementation of Knowles Stored-Energy Function: Theory, Coding and Applications This paper contains the full way of implementing a user-defined hyperelastic constitutive model into the finite element method (FEM) through defining an appropriate elasticity tensor. The Knowles stored-energy potential has been chosen to illustrate the implementation, as this particular potential function proved to be very effective in modeling nonlinear elasticity within moderate deformations. Thus, the Knowles stored-energy potential allows for appropriate modeling of thermoplastics, resins, polymeric composites and living tissues, such as bone for example. The decoupling of volumetric and isochoric behavior within a hyperelastic constitutive equation has been extensively discussed. An analytical elasticity tensor, corresponding to the Knowles stored-energy potential, has been derived. To the best of author's knowledge, this tensor has not been presented in the literature yet. The way of deriving analytical elasticity tensors for hyperelastic materials has been discussed in detail. The analytical elasticity tensor may be further used to develop visco-hyperelastic, nonlinear viscoelastic or viscoplastic constitutive models. A FORTRAN 77 code has been written in order to implement the Knowles hyperelastic model into a FEM system. The performance of the developed code is examined using an exemplary problem.

Parametric Investigation of Mooney-Rivlin Material Constants on Silicone Biocomposite

2017 ◽  
Vol 882 ◽  
pp. 51-55 ◽  
Author(s):  
Siti Humairah Kamarul Bahrain ◽  
Jamaluddin Mahmud
Keyword(s):  
Mechanical Properties ◽  
Constitutive Model ◽  
Future Study ◽  
Mechanical Behaviour ◽  
Constitutive Models ◽  
Material Constant ◽  
High Tendency ◽  
Material Constants ◽  
Hyperelastic Materials ◽  
Linear Behaviour

Hyperelastic materials are unique materials that have high tendency to stretch and its highly non-linear behaviour is commonly investigated using hyperelastic constitutive models. The aim of this paper is to investigate the sensitivity of Mooney-Rivlin material constants; C1 and C2 values in order to observe the behavior and pattern of the stress-stretch graph for silicone-kenaf composite. There were no previous studies done in regards to assess the mechanical behaviour of the stress-stretch curve for silicone-kenaf biocomposite by varying the Mooney-Rivlin material constants. The material constant, C1 and C2 are varied into few cases and the patterns of stress-stretch curves are studied. It was found that variations of C1 and C2 material constants could contribute differently on the mechanical properties of silicone-kenaf composite. Thus, the results and findings of this study could be further enhanced by future study to gain deeper understanding on the hyperelastic materials behaviour and Mooney-Rivlin hyperelastic constitutive model.

scholarly journals Numerical simulations of local and global buckling of hyperelastic tubes with different cross-sections

2018 ◽  
Vol 196 ◽  
pp. 01043
Author(s):  
Łukasz Kowalewski ◽  
Stanisław Jemioło
Keyword(s):  
Numerical Simulations ◽  
Cross Sections ◽  
Constitutive Models ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Initial Stiffness ◽  
Shell Elements ◽  
Hyperelastic Materials ◽  
Global Buckling ◽  
Initial Boundary Value

The aim of the article is to present the application of finite element method (FEM) programs ABAQUS/Standard [1] and ABAQUS/Explicit [2] and the constitutive models of incompressible isotropic hyperelastic materials [3] in the analysis of local and global buckling of axially compressed shell elements made of elastomers. Three FEM models of tubes with the same length and initial stiffness have been created for this purpose. These are tubes with elliptical, square and triangular cross-sections. Three types of constitutive models of a rubber-like (elastomeric) material are used - with the polynomial function of elastic energy in the form of the model MV [3] and standard models of Neo-Hooke and Mooney-Rivlin [4]. No imperfections are introduced in the FEM models of the analyzed pipes. Numerical simulations of buckling of pipes are performed for two types of initial-boundary value problems, i.e. quasi-static and dynamic ones. It has been shown that the type of buckling depends on the cross-section of the pipe. The solutions of buckling of pipes modelling with different constitutive models are compared and good correlations of the results have been observed.

scholarly journals Experimental Characterisation of Hyperelastic Materials for Use in a Passive-Adaptive Membrane on MAVs Wing

2017 ◽  
Vol 54 (4) ◽  
pp. 768-772 ◽  
Author(s):  
Radu Calin Pahonie ◽  
Ciprian Larco ◽  
Mihai Mihaila Andres ◽  
Vasile Nastasescu ◽  
Cristian Barbu ◽  
...  
Keyword(s):  
Large Strain ◽  
Constitutive Models ◽  
Strain Energy Function ◽  
Experimental Tests ◽  
Image Correlation ◽  
Biaxial Test ◽  
Hyperelastic Materials ◽  
Yeoh Model ◽  
Constitutive Material ◽  
Materials Behavior

The paper focuses on the experimental characterization of hyperelastic of the shelf materials in an effort to implement a membrane skin on a low speed asymmetric wing, in order to assess the benefits of flexible lift surfaces. To better determine the best strain energy function definition for the membrane materials, the most notable hyperelastic constitutive models were used together with experimental uniaxial and equiaxial planar tests. For the experimental equi-biaxial test a special loading device was designed and built in the laboratory. The strain measurements for the experimental tests were conducted using digital image correlation, for increased data precision. From the available constitutive material models taken into account, the best for this application proves to be the Yeoh model, as the experimental strain-stress data has a close match for small as well as large strain values. Numerical simulations using finite elements and the Ansys software were performed to predict the materials behavior.

scholarly journals A Hybrid Experimental-Computational Approach to Determine Constitutive Models for Hyperelastic Polymers

2019 ◽  
Author(s):  
Atefe Karimzadeh ◽  
Majid R. Ayatollahi ◽  
Bushroa A. Razak ◽  
Seyed S. R. Koloor ◽  
Mohd Y. Yahya ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Hybrid Approach ◽  
Compressive Loading ◽  
Constitutive Models ◽  
Strain Curve ◽  
Polymeric Materials ◽  
Computational Approach ◽  
Compression Tests ◽  
Stress Strain ◽  
Hyperelastic Materials

A study on the selection of hyperelastic constitutive model for polymeric materials is performed using a hybrid experimental-computational approach. Bis-GMA polymer is used as a case study of hyperelastic material to describe the polymer characteristics by determining its Poisson’s ratio and its valid range of the hyperelastic stress-strain curves. These two parameters are then used to determine the hyperelastic constitutive model by using the hybrid approach. Several uniaxial compression tests along with their finite element simulations are implemented in a systematic way, to identify the polymer behavior under the compressive loading conditions. Nano-indentation experiments are conducted to verify the hyperelastic behavior of the polymer. The experimental and computational evidences confirm that the Poisson’s ratio of Bis-GMA is 0.40 and the appropriate hyperelastic constitutive model for this polymer is of a second order polynomial. It is shown that, the results can be used to determine the true stress-strain curve of hyperelastic materials.

Remarks on nonlinear elastic waves with null conditions

2020 ◽  
Vol 26 ◽  
pp. 121
Author(s):  
Dongbing Zha ◽  
Weimin Peng
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Elastic Waves ◽  
Wave Equations ◽  
Alternative Proof ◽  
Classical Solutions ◽  
Small Initial Data ◽  
Hyperelastic Materials ◽  
Variational Structure ◽  
Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

An Alternative Technique to Evaluate Crack Propagation Path in Hyperelastic Materials

2012 ◽  
Vol 40 (1) ◽  
pp. 42-58 ◽  
Author(s):  
R. R. M. Ozelo ◽  
P. Sollero ◽  
A. L. A. Costa
Keyword(s):  
Constitutive Model ◽  
Crack Propagation ◽  
Experimental Tests ◽  
Growth Direction ◽  
Propagation Path ◽  
J Integral ◽  
Alternative Technique ◽  
Crack Propagation Path ◽  
Hyperelastic Materials ◽  
Material Constitutive Model

Abstract REFERENCE: R. R. M. Ozelo, P. Sollero, and A. L. A. Costa, “An Alternative Technique to Evaluate Crack Propagation Path in Hyperelastic Materials,” Tire Science and Technology, TSTCA, Vol. 40, No. 1, January–March 2012, pp. 42–58. ABSTRACT: The analysis of crack propagation in tires aims to provide safety and reliable life prediction. Tire materials are usually nonlinear and present a hyperelastic behavior. Therefore, the use of nonlinear fracture mechanics theory and a hyperelastic material constitutive model are necessary. The material constitutive model used in this work is the Mooney–Rivlin. There are many techniques available to evaluate the crack propagation path in linear elastic materials and estimate the growth direction. However, most of these techniques are not applicable to hyperelastic materials. This paper presents an alternative technique for modeling crack propagation in hyperelastic materials, based in the J-Integral, to evaluate the crack path. The J-Integral is an energy-based parameter and is applicable to nonlinear materials. The technique was applied using abaqus software and compared to experimental tests.

Sign in / Sign up

Export Citation Format

Share Document