The Effect of Network Structure in the Equation of Rubber Elasticity

1976 ◽  
Vol 49 (5) ◽  
pp. 1232-1237 ◽  
Author(s):  
E. M. Valles ◽  
C. W. Macosko
Keyword(s):  
Shear Modulus ◽  
Temperature Dependence ◽  
Network Structure ◽  
Mechanical Response ◽  
Structural Features ◽  
Model System ◽  
Rubber Elasticity ◽  
Stress Strain ◽  
Good Agreement

Abstract Though the stress, strain, and temperature dependence for an ideal rubber is fairly well established, the relation between network structural features like crosslinks, dangling ends, and entanglements and mechanical response is uncertain. The modulus-structure relations recently derived by Miller and Macosko for several types of networks are tested here with a model system: the hydrosilation crosslinking of vinyl-terminated polydimethylsiloxane chains with a tetra-functional silane. Results of shear modulus as a function of extent of reaction and of stoichiometric imbalance are in good agreement with the theory.

scholarly journals Ability of Constitutive Models to Characterize the Temperature Dependence of Rubber Hyperelasticity and to Predict the Stress-Strain Behavior of Filled Rubber under Different Defor Mation States

Polymers ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 369
Author(s):  
Xintao Fu ◽  
Zepeng Wang ◽  
Lianxiang Ma
Keyword(s):  
Experimental Data ◽  
Temperature Dependence ◽  
Mechanical Response ◽  
Constitutive Models ◽  
Uniaxial Tensile ◽  
Uniaxial Tensile Test ◽  
Chain Model ◽  
Stress Strain ◽  
Filled Rubber ◽  
Yeoh Model

In this paper, some representative hyperelastic constitutive models of rubber materials were reviewed from the perspectives of molecular chain network statistical mechanics and continuum mechanics. Based on the advantages of existing models, an improved constitutive model was developed, and the stress–strain relationship was derived. Uniaxial tensile tests were performed on two types of filled tire compounds at different temperatures. The physical phenomena related to rubber deformation were analyzed, and the temperature dependence of the mechanical behavior of filled rubber in a larger deformation range (150% strain) was revealed from multiple angles. Based on the experimental data, the ability of several models to describe the stress–strain mechanical response of carbon black filled compound was studied, and the application limitations of some constitutive models were revealed. Combined with the experimental data, the ability of Yeoh model, Ogden model (n = 3), and improved eight-chain model to characterize the temperature dependence was studied, and the laws of temperature dependence of their parameters were revealed. By fitting the uniaxial tensile test data and comparing it with the Yeoh model, the improved eight-chain model was proved to have a better ability to predict the hyperelastic behavior of rubber materials under different deformation states. Finally, the improved eight-chain model was successfully applied to finite element analysis (FEA) and compared with the experimental data. It was found that the improved eight-chain model can accurately describe the stress–strain characteristics of filled rubber.

Biaxial Extension Studies Using Inflation of Sheets of Unimodal Model Networks

1990 ◽  
Vol 63 (2) ◽  
pp. 276-284 ◽  
Author(s):  
P. Xu ◽  
J. E. Mark
Keyword(s):  
Experimental Data ◽  
Uniaxial Extension ◽  
Specific Region ◽  
Rubber Elasticity ◽  
Experimental Results ◽  
Stress Strain ◽  
Biaxial Extension ◽  
Extension Ratio ◽  
Model Networks ◽  
Good Agreement

Abstract Measurements of uniaxial extension and compression were made on model poly(dimethylsiloxane) (PDMS) [−Si(CH3)2−O−]x networks to examine the molecular theories of rubber elasticity. The stress-strain isotherms showed that the Flory-Erman theory of rubber elasticity is in good agreement with experimental data from extension to compression (α−1: 0.3–13), while the Mooney-Rivlin relation is useful only in a specific region of extension ratio (α−1: 0.3–0.8). The experimental results strongly support the theory of Flory-Erman, rather than those of phantom and affine networks. It is thus evident that the Flory-Erman theory of rubber elasticity is the more nearly correct.

scholarly journals Visco-Hyperelastic Characterization of the Equine Immature Zona Pellucida

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1223
Author(s):  
Elisa Ficarella ◽  
Mohammad Minooei ◽  
Lorenzo Santoro ◽  
Elisabetta Toma ◽  
Bartolomeo Trentadue ◽  
...  
Keyword(s):  
Zona Pellucida ◽  
Soft Matter ◽  
Mechanical Response ◽  
Mechanical Characterization ◽  
Nonlinear Material ◽  
Prony Series ◽  
Critical Comparison ◽  
Highly Nonlinear ◽  
Good Agreement

This article presents a very detailed study on the mechanical characterization of a highly nonlinear material, the immature equine zona pellucida (ZP) membrane. The ZP is modeled as a visco-hyperelastic soft matter. The Arruda–Boyce constitutive equation and the two-term Prony series are identified as the most suitable models for describing the hyperelastic and viscous components, respectively, of the ZP’s mechanical response. Material properties are identified via inverse analysis based on nonlinear optimization which fits nanoindentation curves recorded at different rates. The suitability of the proposed approach is fully demonstrated by the very good agreement between AFM data and numerically reconstructed force–indentation curves. A critical comparison of mechanical behavior of two immature ZP membranes (i.e., equine and porcine ZPs) is also carried out considering the information on the structure of these materials available from electron microscopy investigations documented in the literature.

A New Look at Measurements of Network Density

1986 ◽  
Vol 59 (1) ◽  
pp. 138-141 ◽  
Author(s):  
Robert A. Hayes
Keyword(s):  
Hysteresis Loop ◽  
Interaction Parameters ◽  
Network Density ◽  
Stress Strain ◽  
Solvent Interaction ◽  
Solvent Method ◽  
Strain Data ◽  
Good Agreement ◽  
Polymer Solvent ◽  
New Look

Abstract A two-solvent method for determining the polymer-solvent interaction parameters independently of stress-strain data is described. The values obtained are much lower than those reported previously. Network densities calculated from swelling data and these interaction parameters are in good agreement with those calculated from the return portion of a hysteresis loop at high elongations.

The Structural Framework of Pictorial Balance

Perception ◽  
1996 ◽  
Vol 25 (12) ◽  
pp. 1419-1436 ◽  
Author(s):  
Paul Locher ◽  
Sharon Gray ◽  
Calvin Nodine
Keyword(s):  
Visual Arts ◽  
Structural Features ◽  
Original Compositions ◽  
The Other ◽  
Global Integration ◽  
Artistic Style ◽  
Structural Framework ◽  
Museum Professionals ◽  
Balance Structure ◽  
Good Agreement

Two experiments were performed to examine how the subjective balance of a painting is created by its structural features and to determine if balance influences the way people look at paintings. Stimuli consisted of sixteen reproductions of twentieth-century paintings varying in artistic style and a reconstructed less-balanced version of each. Participants in experiment 1 determined the location of the balance center of each composition, assigned ‘weights’ to the pictorial features which contributed to the location of the balance center, and rated the picture for balance. It was found that design and museum professionals and individuals untrained in the visual arts were in good agreement as to the structural framework underlying the balance organization of a painting. For all participants, disruption of the balanced organizations of the original compositions led to reliable shifts in the location of the perceived balance centers of the originals compared with their less-balanced perturbations. Additionally, it was observed that particular features as such were not the origin of the balance phenomenon; rather, judgments concerning the balance structure and its center were dependent on the global integration of information across a wide area of the display field, but especially from its central region. Last, the subtle changes in balance structure between versions resulted in lower ratings of balance being assigned to the less-balanced perturbations by the design professionals only; the other two participant groups evaluated overall balance of the versions as comparable. In experiment 2, eye movements of a different group of untrained individuals were recorded as they performed similar tasks on the art stimuli. It was found that disruption of the balance structure of the original representational but not abstract compositions resulted in different regions of the original and perturbed versions being visually explored. Findings of both experiments are related to theoretical notions of balance.

Features of nonlinear in-plane shear deformation of a unidirectional and orthogonally reinforced polymer sheets of composite materials

2021 ◽  
Vol 87 (5) ◽  
pp. 47-55
Author(s):  
A. O. Polovyi ◽  
N. V. Matiushevski ◽  
N. G. Lisachenko
Keyword(s):  
Experimental Data ◽  
Composite Materials ◽  
Shear Modulus ◽  
Maximum Deviation ◽  
Linear Section ◽  
Stress Strain ◽  
Plane Shear ◽  
End Point ◽  
Reinforced Polymer ◽  
Failure Point

A comparative analysis of typical stress-strain diagrams obtained for in-plain shear of the 25 unidirectional and cross-ply reinforced polymer matrix composites under quasi-static loading was carried out. Three of them were tested in the framework of this study, and the experimental data on other materials were taken from the literature. The analysis of the generalized shear-strength curves showed that most of the tested materials exhibit the similar deformation pattern depending on their initial shear modulus: a linear section is observed at the beginning of loading, whereas further increase of the load decreases the slope of the curve reaching the minimum in the failure point. For the three parameters (end point the linear part, maximum reduced deviation of the diagram, tangent shear modulus at the failure point) characterizing the individual features of the presented stress-strain diagrams, approximating their dependences on the value of the reduced initial shear modulus are obtained. At the characteristic points of the deformation diagrams, boundary conditions are determined that can be used to find the parameters of the approximating functions. A condition is proposed for determination of the end point of the linear section on the experimental stress-strain curve, according to which the maximum deviation between the experimental and calculated (according to Hooke’s law) values of the shear stress in this section is no more than 1%, thus ensuring rather high accuracy of approximation on the linear section of the diagram. The results of this study are recommended to use when developing universal and relatively simple in structure approximating functions that take into account the characteristic properties of the experimental curves of deformation of polymer composite materials under in-plane shear of the sheet. The minimum set of experimental data is required to determine the parameters of these functions.

Phase stability, Debye temperature and hardness of semiconducting manganese tetraboride MnB4: First-principles investigations

2017 ◽  
Vol 31 (20) ◽  
pp. 1750131 ◽  
Author(s):  
Ming-Min Zhong ◽  
Cheng Huang ◽  
Chun-Ling Tian
Keyword(s):  
Debye Temperature ◽  
Phase Stability ◽  
First Principles ◽  
Formation Enthalpy ◽  
Structural Features ◽  
High Melting Point ◽  
Fundamental Understanding ◽  
New Perspective ◽  
The Relationship ◽  
Good Agreement

First-principles investigations are employed to provide a fundamental understanding of the structural features, phase stability, mechanical properties, Debye temperature, and hardness of manganese tetraboride. Eight candidate structures of known transition-metal tetraborides are chosen to probe. The calculated lattice parameters, elastic properties, Poisson’s ratio, and [Formula: see text] ratio are derived. It is observed that the monoclinic structure with [Formula: see text] symmetry (MnB4–MnB4) is the most stable in energy. The mechanical and thermodynamic stabilities of seven possible phases are confirmed by the calculated elastic constants and formation enthalpy. Moreover, the analysis on density of states demonstrates semiconducting behavior of MnB4–MnB4 and different metallic behaviors of other phases. The estimated hardness of MnB4–MnB4 is 38.3 GPa, which is in good agreement with experimental value. Furthermore, the relationship between hardness and Debye temperature is investigated and verifies that MnB4–MnB4 is a newly potential semiconducting ultrahard material with high melting point. It provides a new perspective of searching for semiconducting superhard materials to be applied in extreme conditions.

TEMPERATURE-DEPENDENCE OF PROTON CONDUCTIVITY IN HYDROGEN-BONDED MOLECULAR SYSTEMS

2007 ◽  
Vol 21 (19) ◽  
pp. 1239-1252 ◽  
Author(s):  
XIAO-FENG PANG ◽  
BO DENG ◽  
HUAI-WU ZHANG ◽  
YUAN-PING FENG
Keyword(s):  
Experimental Data ◽  
Electric Field ◽  
Temperature Dependence ◽  
Electric Conductivity ◽  
Proton Conductivity ◽  
Model System ◽  
Time Dependent ◽  
Molecular Systems ◽  
Damping Effect ◽  
Hydrogen Bonded

The temperature-dependence of proton electric conductivity in hydrogen-bonded molecular systems with damping effect was studied. The time-dependent velocity of proton and its mobility are determined from the Hamiltonian of a model system. The calculated mobility of (3.57–3.76) × 10-6 m 2/ Vs for uniform ice is in agreement with the experimental value of (1 - 10) × 10-2 m 2/ Vs . When the temperature and damping effects of the medium are considered, the mobility is found to depend on the temperature for various electric field values in the system, i.e. the mobility increases initially and reaches a maximum at about 191 K, but decreases subsequently to a minimum at approximately 241 K, and increases again in the range of 150–270 K. This behavior agrees with experimental data of ice.

Collagen; ultrastructure and its relation to mechanical properties as a function of ageing

1972 ◽  
Vol 180 (1060) ◽  
pp. 293-315 ◽  
Keyword(s):  
Deformation Behaviour ◽  
Life Time ◽  
Periodic Pattern ◽  
Albino Rats ◽  
Structure And Properties ◽  
Stress Strain ◽  
Good Correspondence ◽  
Bearing Unit ◽  
Strain Data ◽  
Good Agreement

Tail tendons from Fischer and Sprague-Dawly albino rats of ages from 2 weeks to 3 years were investigated under the polarizing microscope as regards structure and deformation behaviour. Periodically extinguishing bands were observed along the otherwise featureless tendons. By analysing the behaviour of this extinction pattern under appropriate rotations of the tendon, it could be deduced that the orientation of the basic birefringent units varies periodically along the tendon and that this periodic pattern corresponds to a planar arrangement of the anisotropic entities. All the relevant parameters of this periodic structure could be determined in a representative manner from polarizing optics alone. Subdivision of the tendons revealed regularly undulating or rather crimped subunits in good correspondence to what has been deduced from the extinction bands in the intact tendons. The crimp angle was found to decrease while the periodicity increased - in approximate proportion to the length of the tail - with the age of the rat implying constancy of crimp number during the life time of the animal. On elongation the periodicity was gradually removed. The calculated fibre elongation necessary to eliminate the crimp was in good agreement with observation for mature rats but was larger for young rats implying the simultaneous stretching of the fibre itself. Stress-strain properties of tendons were measured and models for crimp straightening were tested. It was found that a model containing inflexible hinges, corresponding to the ‘elastica’ problem in mechanics gave reasonable fit with experiment. Analysis of stress-strain data on this basis leads to a basic load bearing unit, the diameter of which increases from 100 to 500 nm with the age of the animal. Implications of these findings for the structure and properties of the tendons, also in relation to ageing are pointed out.

scholarly journals Normal spectral emissivity of liquid Al-Ti binary alloys

2020 ◽  
Vol 48 (5-6) ◽  
pp. 423-438
Author(s):  
JUERGEN BRILLO ◽  
JOHANNA J. WESSING ◽  
HIDEKAZU KOBATAKE ◽  
HIROYUKI FUKUYAMA
Keyword(s):  
Temperature Dependence ◽  
Reasonable Agreement ◽  
Spectral Emissivity ◽  
Liquid System ◽  
Normal Spectral Emissivity ◽  
Binary Liquid System ◽  
Binary Liquid ◽  
Electrical Resistivities ◽  
Existing Data ◽  
Good Agreement

The normal spectral emissivity ε of four compositions in the Al-Ti binary liquid system was measured in dependence of the wavelength and temperature. It was found that all compositions show negligible temperature dependence. At a wavelength of 940 nm, the emissivity amounts to 0.37, 0.40, 0.32, and 0.31 for Ti, Al20Ti80, Al50Ti50, and Al70Ti30, respectively. The dependence of the emissivity on composition is in good agreement with literature data of binary and multi-component Al-Ti-based alloys. Using the classical Drude model, electrical resistivities are predicted for the Al-Ti system from the measured emissivities. Comparison with existing data from literature for Al show reasonable agreement.

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