Modeling of the Stress–Birefringence–Stretch Behavior in Rubbers Using the Gent Model

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
A. K. Mossi Idrissa ◽  
S. Ahzi ◽  
Y. Rémond ◽  
J. Gracio
Keyword(s):  
Constitutive Model ◽  
Network Theory ◽  
Elastic Behavior ◽  
Large Strains ◽  
Chain Model ◽  
Complex Formulation ◽  
Gent Model ◽  
New Formulation ◽  
Gaussian Network ◽  
Stretch Response

In this paper, we discuss the application of different stress–optic laws for rubbers to predict the birefringence evolution and the stress–stretch relationship. The main focus of this work is to propose a new formulation for the stress–birefringence relationship using the Gent theory for rubber elasticity. The Gent constitutive model for the stress–stretch response has been shown to provide a nearly equivalent rubber elastic behavior as that of the widely used eight-chain model. By combining the simpler stress–stretch relationship from the Gent model with a Gaussian network theory for birefringence, we propose a simplified stress–optic relationship. We show that our obtained results are in accord with the existing experimental results at large strains. Our proposed simplified formulation and results allow us to conclude that the Gent theory can be extended to predict optical anisotropy evolution under large strains and that these predictions are nearly equivalent to the more complex formulation based on the eight-chain model.

Orthotropic Hyperelasticity in Terms of an Arbitrary Molecular Chain Model

2001 ◽  
Vol 69 (2) ◽  
pp. 198-201 ◽  
Author(s):  
J. E. Bischoff ◽  
E. M. Arruda ◽  
K. Grosh
Keyword(s):  
Constitutive Model ◽  
Strain Energy Function ◽  
Constitutive Law ◽  
Orthotropic Materials ◽  
Chain Model ◽  
Wormlike Chain ◽  
General Terms ◽  
Mechanical Models ◽  
Orthotropic Hyperelasticity ◽  
Wormlike Chain Model

There are many statistical mechanical models of long-chain models, two of which are the freely jointed chain model and the wormlike chain model. A continuum constitutive law for hyperelastic orthotropic materials has recently been developed using the freely jointed chain model as its basis. In this note, the continuum strain energy function is recast in general terms allowing for the incorporation of an arbitrary macromolecular constitutive model. In particular, the orthotropic constitutive model is recast using the wormlike chain model in place of the freely jointed chain model and the effects of this alternation are examined.

Viscoelastic-viscoplastic combined constitutive model for glassy amorphous polymers under loading/unloading/no-load states

2020 ◽  
Vol 37 (5) ◽  
pp. 1703-1735
Author(s):  
Seishiro Matsubara ◽  
Kenjiro Terada ◽  
Ryusei Maeda ◽  
Takaya Kobayashi ◽  
Masanobu Murata ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Deformation Rate ◽  
Amorphous Polymers ◽  
Elastic Behavior ◽  
Content Type ◽  
Rate Dependent ◽  
Proposed Model ◽  
Wide Range ◽  
In Series ◽  
Rheology Model

Purpose This study aims to propose a novel viscoelastic–viscoplastic combined constitutive model for glassy amorphous polymers within the framework of thermodynamics at finite strain that is capable of capturing their rate-dependent inelastic mechanical behavior in wide ranges of deformation rate and amount. Design/methodology/approach The rheology model whose viscoelastic and viscoplastic elements are connected in series is set in accordance with the multi-mechanism theory. Then, the constitutive functions are formulated on the basis of the multiplicative decomposition of the deformation gradient implicated by the rheology model within the framework of thermodynamics. Dynamic mechanical analysis (DMA) and loading/unloading/no-load tests for polycarbonate (PC) are conducted to identify the material parameters and demonstrate the capability of the proposed model. Findings The performance was validated in comparison with the series of the test results with different rates and amounts of deformation before unloading together. It has been confirmed that the proposed model can accommodate various material behaviors empirically observed, such as rate-dependent elasticity, elastic hysteresis, strain softening, orientation hardening and strain recovery. Originality/value This paper presents a novel rheological constitutive model in which the viscoelastic element connected in series with the viscoplastic one exclusively represents the elastic behavior, and each material response is formulated according to the multiplicatively decomposed deformation gradients. In particular, the yield strength followed by the isotropic hardening reflects the relaxation characteristics in the viscoelastic constitutive functions so that the glass transition temperature could be variant within the wide range of deformation rate. Consequently, the model enables us to properly represent the loading process up to large deformation regime followed by unloading and no-load processes.

scholarly journals Johnson–Holmquist-II(JH-2) Constitutive Model for Rock Materials: Parameter Determination and Application in Tunnel Smooth Blasting

2018 ◽  
Vol 8 (9) ◽  
pp. 1675 ◽  
Author(s):  
Jianxiu Wang ◽  
Yao Yin ◽  
Chuanwen Luo
Keyword(s):  
Constitutive Model ◽  
High Pressures ◽  
Numerical Study ◽  
Parameter Determination ◽  
Economic Losses ◽  
Large Strains ◽  
Determination Method ◽  
Rock Materials ◽  
Rock Tunnels ◽  
Smooth Blasting

The Johnson–Holmquist-II(JH-2) model is introduced as the constitutive model for rock materials in tunnel smooth blasting. However, complicated and/or high-cost experiments need to be carried out to obtain the parameters of the JH-2 constitutive model. This study chooses Barre granite as an example to propose a quick and convenient determination method for the parameters of the JH-2 model using a series of computational and extrapolated methods. The validity of the parameters is verified via comparing the results of 3D numerical simulations with laboratory blast-loading experiments. Subsequently, the verified parameter determination method, together with the JH-2 damage constitutive model, is applied in the numerical simulation of smooth blasting in Zigaojian tunnel, Hangzhou–Huangshan high-speed railway. The overbreak/underbreak induced by rock blasting and joints/discontinuities is well estimated through comparing the damage contours resulting from the numerical study with the tunnel profiles measured from the tunnel site. The peak particle velocities (PPVs) of the near field are extracted to estimate the damage scope and damage degree for the surrounding rock mass of the tunnel on the basis of PPV damage criteria. This method can be used in the excavation of rock tunnels subjected to large strains, high strain rates, and high pressures, thereby reducing safety risk and economic losses.

scholarly journals Multiscale Network Modeling of Fibrin Fibers and Fibrin Clots with Protofibril Binding Mechanics

Polymers ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1223
Author(s):  
Sumith Yesudasan ◽  
Rodney D. Averett
Keyword(s):  
Atomic Force Microscopy ◽  
Mechanical Behavior ◽  
Network Model ◽  
Large Strains ◽  
Chain Model ◽  
Force Extension ◽  
Nonlinear Spring ◽  
Force Microscopy ◽  
Atomic Force ◽  
Fibrin Clots

The multiscale mechanical behavior of individual fibrin fibers and fibrin clots was modeled by coupling atomistic simulation data and microscopic experimental data. We propose a new protofibril element composed of a nonlinear spring network, and constructed this based on molecular simulations and atomic force microscopy results to simulate the force extension behavior of fibrin fibers. This new network model also accounts for the complex interaction of protofibrils with one another, the effects of the presence of a solvent, Coulombic attraction, and other binding forces. The network model was formulated to simulate the force–extension mechanical behavior of single fibrin fibers from atomic force microscopy experiments, and shows good agreement. The validated fibrin fiber network model was then combined with a modified version of the Arruda–Boyce eight-chain model to estimate the force extension behavior of the fibrin clot at the continuum level, which shows very good correlation. The results show that our network model is able to predict the behavior of fibrin fibers as well as fibrin clots at small strains, large strains, and close to the break strain. We used the network model to explain why the mechanical response of fibrin clots and fibrin fibers deviates from worm-like chain behavior, and instead behaves like a nonlinear spring.

scholarly journals Toxicity and Antileishmanial Activity of a New Stable Lipid Suspension of Amphotericin B

2003 ◽  
Vol 47 (12) ◽  
pp. 3774-3779 ◽  
Author(s):  
Malika Larabi ◽  
Vanessa Yardley ◽  
Philippe M. Loiseau ◽  
Martine Appel ◽  
Philippe Legrand ◽  
...  
Keyword(s):  
Amphotericin B ◽  
Leishmania Donovani ◽  
Lethal Dose ◽  
Peritoneal Macrophages ◽  
Lipid Complex ◽  
Complex Formulation ◽  
Cd1 Mice ◽  
New Formulation ◽  
Lipid Formulations

ABSTRACT The aim of the present study was to evaluate the toxicity and the activity of a new lipid complex formulation of amphotericin B (AMB) (LC-AMB; dimyristoyl phosphatidylcholine, dimyristoyl phosphatidylglycerol, and AMB) that can be produced by a simple process. Like other lipid formulations, this new complex reduced both the hemolytic activity of AMB (the concentration causing 50% hemolysis of human erythrocytes, >100 μg/ml) and its toxicity toward murine peritoneal macrophages (50% inhibitory concentration, >100 μg/ml at 24 h). The in vivo toxicity of the new formulation (50% lethal dose,> 200 mg/kg of body weight for CD1 mice) was similar to those of other commercial lipid formulations of AMB. The complex was the most effective formulation against the DD8 strain of Leishmania donovani. It was unable to reverse the resistance of an AMB-resistant L. donovani strain. In vivo LC-AMB was less efficient than AmBisome against L. donovani.

Phenomenological Hyperelastic Strain-Stiffening Constitutive Models for Rubber

2006 ◽  
Vol 79 (1) ◽  
pp. 152-169 ◽  
Author(s):  
Cornelius O. Horgan ◽  
Giuseppe Saccomandi
Keyword(s):  
Boundary Value Problems ◽  
Soft Tissues ◽  
Boundary Value ◽  
Constitutive Models ◽  
Biological Tissues ◽  
Large Strains ◽  
Shear Mode ◽  
Crack Problems ◽  
Gent Model ◽  
Constitutive Parameters

Abstract Many rubber-like materials and soft biological tissues exhibit a significant stiffening or hardening in their stress-strain curves at large strains. The accurate modeling of this phenomenon is a key issue for a better understanding of the thermomechanics of rubber and the biomechanics of soft tissues. In this paper, we provide a review of some phenomenological hyperelastic constitutive models that have been proposed to model this strain stiffening effect and summarize recent advances in the solution of boundary-value problems that illustrate the utility of such models. The emphasis is on constitutive models that reflect limiting chain extensibility at the molecular level. A remarkably simple phenomenological model of this type has been proposed by Gent. The Gent model has a molecular basis related to the inverse Langevin function compact support non-Gaussian statistics for the end-to-end distance function. The mathematical simplicity of the Gent model, which contains just two constitutive parameters, has facilitated the analytic solution of a variety of specific boundary-value problems that are relevant to the rubber industry and we summarize the main results here. These problems include those of torsion, axial, azimuthal and helical shear, anti-plane shear, mode III crack problems, rotation induced deformation of circular cylinders and fracture problems. It is shown that the results are radically different from those obtained in the literature for classical models such as the neo-Hookean and Mooney-Rivlin models for incompressible rubber. Extensions to include thermoelasticity, material compressibility, anisotropy and stress softening are also briefly described.

A Directional Damage Constitutive Model for Stress-Softening in Solid Propellant

2020 ◽  
Author(s):  
Yang Chen ◽  
Vahid Morovati ◽  
Roozbeh Dargazany
Keyword(s):  
Constitutive Model ◽  
Mechanical Model ◽  
Solid Propellant ◽  
Network Evolution ◽  
Elastic Behavior ◽  
Plastic Behavior ◽  
Solid Propellants ◽  
Softening Effect ◽  
Stress Softening ◽  
Highly Nonlinear

Abstract Solid propellants are particulate composite with a light cross-linked elastomeric binder filled with a high concentration of energetic, solid aggregates. Solid propellants are often considered as highly nonlinear elastomeric materials, with elastic behavior resulted from its binder and plastic behavior from its energetic particles. The study of the micro-structure and mechanical properties of solid propellant is crucial for its design, safety evaluation, and lifetime prediction of solid fuel carriers. The constitutive model proposed for rubber-like material can often be generalized to predict the nonlinear behavior of solid propellant due to the dependency on the mechanical behavior of solid propellant on its elastomeric binder material. This paper focuses on developing a model that predicts the stress softening and strain-residual mechanism of the solid propellant. This micro-mechanical model for solid propellant was proposed based on the network evolution theory. The motivation of this study is the lack of a micro-mechanical model that can describe both the stress softening effect and strain residual in the quasi-static behavior of propellants. The simplified network-evolution model with only five parameters is a simple micro-mechanical model that captures both the stress softening effect and strain residual. Besides the simplicity and reduced fitting procedure, the model was validated against several experimental data and illustrated good agreement in small and large deformations, making the proposed model a suitable option for commercial and other applications.

Sign in / Sign up

Export Citation Format

Share Document