Direct Comparison of the Gent and the Arruda-Boyce Constitutive Models of Rubber Elasticity

1996 ◽  
Vol 69 (5) ◽  
pp. 781-785 ◽  
Author(s):  
Mary C. Boyce
Keyword(s):  
Constitutive Model ◽  
Large Strain ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Rubber Elasticity ◽  
Elastic Materials ◽  
Material Constants ◽  
Salient Features

Abstract The Arruda and Boyce eight-chain network constitutive model for rubber elastic materials is compared to the new Gent constitutive model for rubber elasticity. The salient features of each of the two models are compared. The ability of both models to predict three dimensional large strain deformation is demonstrated showing the near equivalence of these two model constructions as well as their abilities to predict complex three-dimensional deformation with only two material constants.

scholarly journals A Comparison of the Hart-Smith Model with Arruda-Boyce and Gent Formulations for Rubber Elasticity

2004 ◽  
Vol 77 (4) ◽  
pp. 724-735 ◽  
Author(s):  
G. Chagnon ◽  
G. Marckmann ◽  
E. Verron
Keyword(s):  
Constitutive Model ◽  
Large Strain ◽  
Constitutive Models ◽  
Rubber Elasticity ◽  
Material Parameters ◽  
Strain Responses ◽  
Smith Model

Abstract The present paper demonstrates that the Hart-Smith constitutive model and the more recent Arruda and Boyce eight chains and Gent constitutive models are closely related. The ability of these three models to predict both small and large strain responses of rubbers is highlighted and equations that relate their material parameters are established.

A Modified Microplane Model Using Transformation Surfaces to Consider Loading History on Phase Transition in Shape Memory Alloys

2014 ◽  
Author(s):  
Milad Shirani ◽  
Reza Mehrabi ◽  
Masood Taheri Andani ◽  
Mahmoud Kadkhodaei ◽  
Mohammad Elahinia ◽  
...  
Keyword(s):  
Free Energy ◽  
Constitutive Model ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Phenomenological Approach ◽  
Material Point ◽  
Loading History ◽  
Energy Potential ◽  
Microplane Model ◽  
Thermodynamic Driving Force

In most of the existing SMA constitutive models, it is assumed that transformation starts when a thermodynamic driving force reaches a specified amount regardless of loading history. In this work, a phenomenological approach is used to develop an enhanced one-dimensional constitutive model in which loading history is directly considered as one of the main parameters affecting the transformation start conditions. To generalize the model to three-dimensional cases, a microplane formulation based on volumetric-deviatoric is employed. A free energy potential is defined at the microplane level, integrated over all orientations at a material point to provide the macroscopic free energy. Experiments are carried out on Nitinol superelastic tubes to validate the newly proposed constitutive model. In these experiments, interruptions are applied during transformations to show the effects of loading history on transformation start conditions. Numerical results are compared with the experimental data to demonstrate the accuracy of the enhanced model.

An Efficient Method for the Optimization of Viscoplastic Constitutive Model Constants

2010 ◽  
Author(s):  
James P. DeMarco ◽  
Erik A. Hogan ◽  
Calvin M. Stewart ◽  
Ali P. Gordon
Keyword(s):  
Constitutive Model ◽  
Random Noise ◽  
Constitutive Models ◽  
Optimization Method ◽  
Complex Stress ◽  
Operating Conditions ◽  
Widespread Application ◽  
Material Constants ◽  
Material Parameters ◽  
Critical Components

Constitutive modeling has proven useful in providing accurate predictions of material response in components subjected to a variety of operating conditions; however, the high number of experiments necessary to determine appropriate constants for a model can be prohibitive, especially for more expensive materials. Generally, up to twenty experiments simulating a range of conditions are needed to identify the material parameters for a model. In this paper, an automated process for optimizing the material constants of the Miller constitutive model for uniaxial modeling is introduced. The use of more complex stress, strain, and temperature histories than are traditionally used allows for the effects of all material parameters to be captured using significantly fewer tests. A graphical user interface known as uSHARP was created to implement the resulting method, which determines the material constants of a viscoplastic model using a minimum amount of experimental data. By carrying out successive finite element simulations and comparing the results to simulated experimental test data, both with and without random noise, the material constants were determined from 75% fewer experiments. The optimization method introduced here reduces the cost and time necessary to determine constitutive model constants through experimentation. Thus it allows for a more widespread application of advanced constitutive models in industry and for better life prediction modeling of critical components in high-temperature applications.

scholarly journals A Rheological Model of Sandstones considering Response to Thermal Treatment

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Xingang Wang ◽  
Lei Huang ◽  
Junrong Zhang
Keyword(s):  
Thermal Treatment ◽  
Constitutive Model ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Energy Utilization ◽  
Elastic Response ◽  
Structure Damage ◽  
Rheological Response ◽  
Different Temperatures ◽  
Thermally Treated

Time-dependent rheological response of geomaterials to thermal treatment is a crucial issue in geothermal energy utilization and deep mineral mining. This response, however, has not yet been fully considered in the existing rheological constitutive models for sandstones. In order to experimentally investigate such responses and establish the associated rheological constitutive model, this study considers the sandstone specimens which have been thermally treated under different temperatures. The triaxial rheological test in conjunction with the scanning electron microscope is employed in the investigation to observe the mechanically and macro-/micromorphologically rheological response. Investigation results show that the thermal treatment induces microcracks and microdefects, and subsequently, they propagate during the creep. As a consequence, the heterogeneous deformation occurs, and macrocracks are present, leading to the irregular fluctuation and mutation in strain over time. A higher temperature contributes to a more severe structure damage and in turn reduces the intactness of sandstones and elevates the rheological response. The investigation allows successful establishment of a three-dimensional constitutive equation considering the instantaneous elastic response to thermal treatment. Based on the equation, a nonlinear visco-elastoplastic rheological constitutive model is developed for sandstones. Comparison with three existing rheological models shows that the model developed in this study could well represent the rheological process of the thermally treated sandstones.

A Large Strain Hyperelastic Constitutive Model for Intraluminal Thrombus From Abdominal Aortic Aneurysm

1999 ◽  
Author(s):  
David H. J. Wang ◽  
Michel S. Makaroun ◽  
Marshall W. Webster ◽  
David A. Vorp
Keyword(s):  
Abdominal Aortic Aneurysm ◽  
Aortic Aneurysm ◽  
Constitutive Model ◽  
Large Strain ◽  
Constitutive Models ◽  
Wall Stress ◽  
Accurate Estimation ◽  
Elastic Model ◽  
Intraluminal Thrombus ◽  
Abdominal Aortic

Abstract Rupture of abdominal aortic aneurysm (AAA) occurs when the wall stress acting on the dilated aortic wall exceeds the strength of the tissue. Therefore, accurate estimation of the wall stress distribution in AAA may be a clinically useful tool to predict their rupture. A majority of AAA contains a laminated, stationary, intraluminal thrombus (ILT) (Harter et al., 1982). Previous investigations have shown that ILT may significantly alter the wall stress acting on AAA (Inzoli et al., 1993; Mower et al., 1997; Stringfellow et al., 1987; Vorp et al., 1998; Di Martino et al., 1998). However, all of those studies used a simplified linear elastic model for ILT. This is inappropriate and can lead to inaccuracies since both AAA wall and contained ILT undergo large deformation during the cardiac cycle (Vorp et al., 1996). Therefore, to accomplish accurate stress analysis of AAA, appropriate constitutive models for both the wall and ILT are necessary. Our group has previously proposed a finite strain constitutive model for the AAA wall (Raghavan et al., in press). The purpose of this work was to derive a more suitable constitutive model and the associated mechanical properties for the ILT within AAA.

Non-Coaxial Plasticity Constitutive Modeling of Sands

2013 ◽  
Vol 684 ◽  
pp. 150-153 ◽  
Author(s):  
Ping Hu ◽  
Mao Song Huang ◽  
Deng Gao Wu
Keyword(s):  
Plastic Strain ◽  
Constitutive Model ◽  
Principal Stress ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Strain Increment ◽  
Stress Axis ◽  
Shear Tests ◽  
Plastic Strain Increment ◽  
Principal Axes

Classical coaxial plasticity constitutive models implicate an inevitable limitation that directions for principal stress and that for principal plastic strain increment are always coaxial. They are not capable of simulating non-coaxial phenomena during the rotation of principal stress axis. In this paper, a three-dimensional, non-coaxial plasticity constitutive model for sands with a modification of Lade angle dependent shape function is introduced to describe the non-coaxial behavior under principal axes rotation. A series of numerical simulations of hollow cylindrical torsional shear tests are performed. The results show that the proposed constitutive model can predict the variations of principal plastic strain increment directions with principal stress directions reasonably.

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.

Finite Strain Viscoplasticity Based on Unified Constitutive Equations and Decomposition of Logarithmic Strain: Applications to Shells

1997 ◽  
Vol 50 (11S) ◽  
pp. S184-S192 ◽  
Author(s):  
C. Sansour ◽  
F. G. Kollmann
Keyword(s):  
Finite Strain ◽  
Large Strain ◽  
Strain Tensor ◽  
Three Dimensional ◽  
Constitutive Models ◽  
Strain Range ◽  
Basic Feature ◽  
Point Of View ◽  
Logarithmic Strain ◽  
Additive Structure

The paper is concerned with a formulation of large strain viscoplasticity based on the concept of unified constitutive models as well as on an additive decomposition of a logarithmic strain tensor. The constitutive model due to Bodner and Partom is modified as to fit within the theoretical framework presented. A basic feature of the formulation is the fact that the additive structure of the infinitesimal theory is preserved in the finite strain range. Based on an essential result, a closed form of the tangent operator is derived which is very efficient from the numerical point of view. As an application, finite shell deformations are considered. The shell theory used allows for the application of three-dimensional constitutive laws and is geometrically exact. The computations are based on an enhanced strain functional where the right Cauchy-Green tensor is enhanced. Two examples of large shell deformations including loading-unloading cycles are presented.

Investigation on the Large Strain Elastoplastic Constitutive Model with Logarithmic Stress Rate Based on Torsion Experiments

2009 ◽  
Vol 417-418 ◽  
pp. 413-416
Author(s):  
Li Hong Yang ◽  
Guang Ping Zou ◽  
Li Ping Yang ◽  
Xue Yi Zhang
Keyword(s):  
Constitutive Model ◽  
Large Strain ◽  
Constitutive Models ◽  
Strain Range ◽  
Torsion Test ◽  
Stress Rate ◽  
Isotropic Hardening ◽  
Kirchhoff Stress ◽  
Elastoplastic Constitutive Model ◽  
Rate Type

A complete analysis was made for an isotropic hardening rate-type elastoplastic constitutive model with the logarithmic stress rate utilizing solid shafts torsion test in the large strain range. The deformation rate, the logarithmic spin, the Kirchhoff stress and the logarithmic stress rate of the Kirchhoff stress were obtained for the free-end solid shaft torsion test when considering Swift effect. Utilizing the results obtained from the solid shaft torsion test, the plastic rigidity function in the isotropic hardening elastoplastic constitutive model was determined at finite strain range. It was shown that the influence of Swift effect on finite strain constitutive model was related to the varying rate of axial deformation and the varying rate of radius deformation to shear strain, and the plastic rigidity function corresponding to the logarithmic stress rate was the same as that corresponding to the Jaumann stress rate when neglecting Swift effect. Solid shaft can achieve very large strain without buckling in torsion test. They can be used to accurately determine the large strain elastoplastic behavior [1-3]. Many researchers are interesting in the theoretical study and experimental study on large strain torsion deformation [1-7]. Jaumann objective stress rate is often adopted for study on constitutive models [1], but Nagtegaa J C [8] discovered that Jaumann stress rate may render oscillatory stress response for anisotropic kinematics hardening simple shear problem. After that, great interests focus on the issues of choosing an appropriate objective stress rate in rate type constitutive models. The expression of logarithmic stress rate with logarithmic spin can be found in Xiao H [9]. It had been proved that among all rate type elastoplastic constitutive models, only those with the newly discovered logarithmic stress rate fulfill the self-consistency criterion. In this paper, the parameter in large strain isotropic hardening elastoplastic constitutive model is determined with logarithmic rate of Kirchhoff stress utilizing solid shaft torsion test.

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