The mechanics and mathematics of the effect of pressure on the shear modulus of elastomers

2009 ◽  
Vol 465 (2112) ◽  
pp. 3859-3874 ◽  
Author(s):  
K. R. Rajagopal ◽  
Giuseppe Saccomandi
Keyword(s):  
Experimental Data ◽  
Shear Modulus ◽  
Classical Theory ◽  
Constitutive Models ◽  
Elastic Response ◽  
Elastic Bodies ◽  
Starting Point ◽  
Elastomeric Materials ◽  
Limiting Chain Extensibility ◽  
And Mathematics

In this paper, we discuss the need for models that express the stretch (or strain) as a function of stress, or implicit constitutive models that relate the stretch (or strain) and stress, for describing the elastic response of some elastomers. We would like to provide an explanation for some experimental data for elastomeric materials that imply that the material moduli depend on pressure. Included in the class of models that are proposed are those which can explain limiting chain extensibility that is exhibited by some rubber-like solids. The models that are proposed stem from a completely different starting point from that for classical elastic bodies, so that these models cannot be obtained within the context of classical 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.

Theoretical determination of the structures of CaSiO3 perovskites

2006 ◽  
Vol 62 (6) ◽  
pp. 1025-1030 ◽  
Author(s):  
Razvan Caracas ◽  
Renata M. Wentzcovitch
Keyword(s):  
Crystal Structure ◽  
Experimental Data ◽  
Density Functional Theory ◽  
Density Functional ◽  
Theoretical Determination ◽  
Functional Theory ◽  
Starting Point ◽  
Atomic Coordinates ◽  
The Ideal

Density functional theory is used to determine the possible crystal structure of the CaSiO3 perovskites and their evolution under pressure. The ideal cubic perovskite is considered as a starting point for studying several possible lower-symmetry distorted structures. The theoretical lattice parameters and the atomic coordinates for all the structures are determined, and the results are discussed with respect to experimental data.

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.

From Adatom Migration to Chemical Kinetics: Models for MBE, Mombe and MOCVD

1993 ◽  
Vol 312 ◽  
Author(s):  
D. D. Vvedensky ◽  
T. Shitarat ◽  
P. Smilauer ◽  
T. Kaneko ◽  
A. Zangwill
Keyword(s):  
Experimental Data ◽  
Molecular Beam Epitaxy ◽  
Molecular Beam ◽  
Chemical Vapor ◽  
High Energy ◽  
Atomic Scale ◽  
Basic Model ◽  
Mobile Species ◽  
Local Environments ◽  
Starting Point

AbstractThe application of Monte Carlo simulations to various epitaxial growth methods is examined from the standpoint of incorporating only those kinetics processes that are required to explain experimental data. A basic model for molecular-beam epitaxy (MBE) is first introduced and some of the features that make it suitable for describing atomic-scale processes are pointed out. Extensions of this model for cases where the atomic constituents of the growing surface are delivered in the form of heteroatomic molecules are then considered. The experimental scenarios that is discussed is the homoepitaxy of GaAs(001) using metalorganic molecular-beam epitaxy (MOMBE) with triethylgallium (TEG) and precursors and using MOCVD with trimethylgallium (TMG). For MOMBE, the comparisons between simulations and experiments are based on reflection high-energy electron diffraction intensities, by analogy with comparisons made for MBE, while for metalorganic chemical vapor deposition (MOCVD) the simulations are compared to in situ glancingincidence x-ray scattering measurements. In both of these cases, the inclusion of a second mobile species to represent the precursor together with various rules for the decomposition of this molecule (in terms of rates and local environments) with be shown to provide a useful starting point for explaining the general trends in the experimental data and for further refinements of the model.

scholarly journals Etnografia como campo de pesquisa na e para a prática docente de professores indígenas Iny-Karajá que ensinam Ciências e Matemática

2021 ◽  
Vol 11 (1) ◽  
pp. 163
Author(s):  
Raimundo Ribeiro dos Santos ◽  
Elisângela Aparecida Aparecida Pereira de Melo
Keyword(s):  
Indigenous People ◽  
Cultural Practices ◽  
Community Context ◽  
Daily Lives ◽  
Mato Grosso ◽  
School Activities ◽  
The People ◽  
Narrative Interview ◽  
Starting Point ◽  
And Mathematics

Este trabalho é proveniente de um estudo desenvolvido na Comunidade Indígena Itxala, município de Santa Terezinha, Estado de Mato Grosso, acerca das práticas socioculturais empreendidas pelos indígenas Iny-Karajá em distintas atividades cotidianas que contemplam as paisagens de manifestações culturais e originárias do povo das águas. Como ponto de partida, trazemos a seguinte indagação: Em que termos é possível etnografar os saberes originários do povo Iny-Karajá na perspectiva de mobilizar e potencializar ações educativas para a sala de aula? Nesse sentido, objetivamos descrever as práticas socioculturais que podem mobilizar e potencializar atividades para o ensino de Ciências e Matemática. O estudo pauta-se na abordagem qualitativa de cunho etnográfico, permitindo evidenciar as impressões e as percepções dos professores, por meio da entrevista narrativa e da participação para observar o cotidiano desses indígenas no decurso da realização de suas práticas socioculturais, com destaque para as pinturas corporais e as ações educativas. Nossas reflexões evidenciam, dentre outras possibilidades, o compartilhar de novos conhecimentos e de atividades escolares na e para a sala de aula mediadas por elementos socioculturais do contexto comunitário, emergindo a negociação de significados como estratégia mediadora e potencializadora do aprendizado de Ciências e Matemática no contexto escolar local.Palavras-chave: Práticas socioculturais. Atividades educativas. Ensino de Ciências e Matemática. Abstract: This work comes from a study developed in the Itxala Indigenous Community, located in the municipality of Santa Terezinha, State of Mato Grosso, Brazil. It is focused on addressing socio-cultural practices of the Iny-Karajá indigenous people during their different daily activities, which include cultural and original manifestations of the people of the waters. As a starting point, we bring the following question: How is it possible to know, through ethnography, the knowledge originating from the Iny-Karajá people in the perspective of mobilizing and enhancing educational actions for the classroom? So, we aim to describe the socio-cultural practices that can mobilize and enhance activities for the teaching of Science and Mathematics. This study is based on a qualitative ethnographic approach, allowing to evidence the impressions and perceptions of teachers through narrative interview and participation, with the intention of observing the daily lives of these indigenous people during the performance of their socio-cultural practices, with emphasis on body paintings and educational actions. Among other possibilities, our reflections show the sharing of new knowledge and school activities in and for the classroom, mediated by sociocultural elements of the community context, making the negotiation of meanings emerge as a mediating and enhancing strategy for the learning of Sciences and Mathematics in the local school context.Keywords: Sociocultural practices. Educational activities. Science and Mathematics Teaching.

Experimental and Numerical Investigations on Hot Deformation Behavior and Processing Maps for ASS 304 and ASS 316

2018 ◽  
Vol 37 (9-10) ◽  
pp. 873-888 ◽  
Author(s):  
Nitin Kotkunde ◽  
Hansoge Nitin Krishnamurthy ◽  
Swadesh Kumar Singh ◽  
Gangadhar Jella
Keyword(s):  
Experimental Data ◽  
Strain Rate ◽  
Hot Deformation ◽  
Deformation Behavior ◽  
Constitutive Models ◽  
Tensile Tests ◽  
Uniaxial Tensile ◽  
Processing Maps ◽  
Hot Deformation Behavior ◽  
Statistical Measures

AbstractA thorough understanding of hot deformation behavior plays a vital role in determining process parameters of hot working processes. Firstly, uniaxial tensile tests have been performed in the temperature ranges of 150 °C–600 °C and strain rate ranges of 0.0001–0.01s−1 for analyzing the deformation behavior of ASS 304 and ASS 316. The phenomenological-based constitutive models namely modified Fields–Backofen (m-FB) and Khan–Huang–Liang (KHL) have been developed. The prediction capability of these models has been verified with experimental data using various statistical measures. Analysis of statistical measures revealed KHL model has good agreement with experimental flow stress data. Through the flow stresses behavior, the processing maps are established and analyzed according to the dynamic materials model (DMM). In the processing map, the variation of the efficiency of the power dissipation is plotted as a function of temperature and strain rate. The processing maps results have been validated with experimental data.

Using Exponential Cubic Splines to Predict Low Temperature Behavior of Elastomeric Materials

1994 ◽  
Author(s):  
Terry E. Shoup ◽  
George R. Fegan
Keyword(s):  
Experimental Data ◽  
Elastic Modulus ◽  
Low Temperatures ◽  
Analytical Techniques ◽  
High Sensitivity ◽  
Considerable Difficulty ◽  
Spline Curves ◽  
Different Types ◽  
Elastomeric Materials ◽  
Energy Absorbing

Abstract Because of their desirable elastic and energy absorbing properties, elastomeric materials have been widely used as shock mounts and pressure seals. The high sensitivity of the elastic modulus of these materials to changes in temperature has been a source of considerable difficulty to the development of robust design methods based on analytical techniques. This paper presents a simple analytical method for predicting the elastic modulus for a group of five different types of elastomers when used at low temperatures. The method is based on the application of exponential cubic spline curves to smooth experimental data. The method is applied to experimental data from the literature to illustrate its usefulness.

Intermolecular Effects: I. The Constrained-Junction Model

1997 ◽  
Author(s):  
Burak Erman ◽  
James E. Mark
Keyword(s):  
Experimental Data ◽  
Free Energy ◽  
Tensile Strain ◽  
Theoretical Models ◽  
Rigorous Derivation ◽  
Starting Point ◽  
Link Model ◽  
A Chain ◽  
Network Modulus ◽  
Degree Of Entanglement

The classical theories of rubber elasticity presented in chapter 2 are based on a hypothetical chain which may pass freely through its neighbors as well as through itself. In a real chain, however, the volume of a segment is excluded to other segments belonging either to the same chain or to others in the network. Consequently, the uncrossability of chain contours by those occupying the same volume becomes an important factor. This chapter and the following one describe theoretical models treating departures from phantom-like behavior arising from the effect of entanglements, which result from this uncrossability of network chains. The chains in the un-cross-linked bulk polymer are highly entangled. These entanglements are permanently fixed once the chains are joined during formation of the network. The degree of entanglement, or degree of interpenetration, in a network is proportional to the number of chains sharing the volume occupied by a given chain. This is quite important, since the observed differences between experimental results on real networks and predictions of the phantom network theory may frequently be attributed to the effects of entanglements. The decrease in network modulus with increasing tensile strain or swelling is the best-known effect arising from deformation-dependent contributions from entanglements. The constrained-junction model presented in this chapter and the slip-link model presented in chapter 4 are both based on the postulate that, upon stretching, the space available to a chain along the direction of stretch is increased, thus resulting in an increase in the freedom of the chain to fluctuate. Similarly, swelling with a suitable diluent separates the chains from one another, decreasing their correlations with neighboring chains. Experimental data presented in figure 3.1 show that the modulus of a network does indeed decrease with both swelling and elongation, finally becoming independent of deformation, as should be the case for the modulus of a phantom network. Rigorous derivation of the modulus of a network from the elastic free energy for this case will be given in chapter 5. The starting point of the constrained-junction model presented in this chapter is the elastic free energy.

scholarly journals Temperature Effect on the Compressive Behavior and Constitutive Model of Plain Hardened Concrete

Materials ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 2801 ◽  
Author(s):  
Ayman El-Zohairy ◽  
Hunter Hammontree ◽  
Eddie Oh ◽  
Perry Moler
Keyword(s):  
Experimental Data ◽  
Compressive Strength ◽  
Temperature Effect ◽  
Modulus Of Elasticity ◽  
Constitutive Models ◽  
Ultimate Strain ◽  
Effect Of Temperature ◽  
Hardened Concrete ◽  
Compressive Behavior ◽  
Stress Strain

Concrete is one of the most common and versatile construction materials and has been used under a wide range of environmental conditions. Temperature is one of them, which significantly affects the performance of concrete, and therefore, a careful evaluation of the effect of temperature on concrete cannot be overemphasized. In this study, an overview of the temperature effect on the compressive behavior of plain hardened concrete is experimentally provided. Concrete cylinders were prepared, cured, and stored under different temperature conditions to be tested under compression. The stress–strain curve, mode of failure, compressive strength, ultimate strain, and modulus of elasticity of concrete were evaluated between the ages of 7 and 90 days. The experimental results were used to propose constitutive models to predict the mechanical properties of concrete under the effect of temperature. Moreover, previous constitutive models were examined to capture the stress–strain relationships of concrete under the effect of temperature. Based on the experimental data and the proposed models, concrete lost 10–20% of its original compressive strength when heated to 100 °C and 30–40% at 260 °C. The previous constitutive models for stress–strain relationships of concrete at normal temperatures can be used to capture these relationships under the effect of temperature by using the compressive strength, ultimate strain, and modulus of elasticity affected by temperature. The effect of temperature on the modulus of elasticity of concrete was considered in the ACI 318-14 equation by using the compressive strength affected by temperature and the results showed good agreement with the experimental data.

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