Constitutive Models for Rubber XII (original) (raw)
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Mechanics of Materials, 2002
The rate-dependent behavior of natural and high damping rubbers is investigated in the compression regime. The experimental results demonstrate the prominence of the rate-dependent high initial stiffness feature in high damping rubber at low stretch level. A modified hyperelastic model is proposed to represent the rate-independent elastic responses including the high initial stiffness feature. A comparative evaluation is carried out to display the better performance of the proposed hyperelastic model than conventional ones over the strain range in representing the equilibrium and the instantaneous responses. The hyperelastic model is incorporated in a finite deformation rate-dependent model structure. A parameter identification scheme is proposed to identify the parameters for the equilibrium and instantaneous responses from the experimental data. The difficulties of direct application of infinitely fast or slow loading rate to such highly viscous materials to obtain these responses and thereby to identify the nonlinear elastic parameters are overcome. The proposed scheme is applied to three types of specimens including natural rubber and high damping rubber. Finally, numerical results obtained from the finite deformation rate-dependent model are compared with the test results to verify the adequacy and robustness of the proposed parameter identification scheme.
A Review of Constitutive Models for Rubber-Like Materials
American J. of Engineering and …, 2010
Problem statement: This study reviewed the needs of different constitutive models for rubber like material undergone large elastic deformation. The constitutive models are widely used in Finite Element Analysis (FEA) packages for rubber components. Most of the starting point for modeling of various kinds of elastomer is a strain energy function. In order to define the hyperelastic material behavior, stress-strain response is required to determine material parameters in the strain energy potential and also proper selection of rubber elastic material model is the first attention. Conclusion: This review provided a sound basis decision to engineers and manufactures to choose the right model from several constitutive models based on strain energy potential for incompressible and isotropic materials.
CONSTITUTIVE MODELS OF RUBBER ELASTICITY: A REVIEW
A review of constitutive models for the finite deformation response of rubbery materials is given. Several recent and classic statistical mechanics and continuum mechanics models of incompressible rubber elasticity are discussed and compared to experimental data. A hybrid of the Flory-Erman model for low stretch deformation and the Arruda-Boyce model for large stretch deformation is shown to give an accurate, predictive description of Treloar's classical data over the entire stretch range for all deformation states. The modelling of compressibility is also addressed.
Hyperelastic models for the description and simulation of rubber subjected to large tensile loading
Archives of Materials Science and Engineering, 2021
Purpose: Rubber is widely used in tires, mechanical parts, and user goods where elasticity is necessary. Some essential features persist unsolved, primarily if they function in excessive mechanical properties. It is required to study elastomeric Rubber's performance, which is operational in high-level dynamic pressure and high tensile strength. These elastomeric aims to increase stress breaking and preserve highly pressurised tensile strength. Design/methodology/approach: The effects of carbon black polymer matrix on the tensile feature of different Rubber have been numerically investigated in this research. Rubber's material characteristics properties were measured using three different percentages (80%, 90%and 100%) of carbon black filler parts per Hundreds Rubber (pphr). Findings: This study found that the tensile strength and elongation are strengthened as the carbon black filler proportion increases by 30%. Practical implications: This research study experimental tests for Rubber within four hyperelastic models: Ogden's Model, Mooney-Rivlin Model, Neo Hooke Model, Arruda-Boyce Model obtain the parameters for the simulation of the material response using the finite element method (FEM) for comparison purposes. These four models have been extensively used in research within Rubber. The hyperelastic models have been utilised to predict the tensile test curves—the accurate description and prediction of elastomer rubber models. For four models, elastomeric material tensile data were used in the FEA package of Abaqus. The relative percentage error was calculated when predicting fitness in selecting the appropriate model—the accurate description and prediction of elastomer rubber models. For four models, elastomeric material tensile data were used in the FEA package of Abaqus. The relative percentage error was calculated when predicting fitness in selecting the appropriate model. Numerical Ogden model results have shown that the relative fitness error was the case with large strains are from 1% to 2.04%. Originality/value: In contrast, other models estimate parameters with fitting errors from 2.3% to 49.45%. The four hyperelastic models were tensile test simulations conducted to verify the efficacy of the tensile test. The results show that experimental data for the uniaxial test hyperelastic behaviour can be regenerated effectively as experiments. Ultimately, it was found that Ogden's Model demonstrates better alignment with the test data than other models.
International Journal of Plasticity, 2006
The rate-dependent behavior of filled natural rubber (NR) and high damping rubber (HDR) is investigated in compression and shear regimes. In order to describe the viscosity-induced rate-dependent effects, a constitutive model of finite strain viscoelasticity founded on the basis of the multiplicative decomposition of the deformation gradient tensor into elastic and inelastic parts is proposed. The total stress is decomposed into an equilibrium stress and a viscosity-induced overstress by following the concept of the Zener model. To identify the constitutive equation for the viscosity from direct experimental observations, an analytical scheme that ascertains the fundamental relation between the inelastic strain rate and the overstress tensor of the Mandel type by evaluating simple relaxation test results is proposed. Evaluation of the experimental results using the proposed analytical scheme confirms the necessity of considering both the current overstress and the current deformation as variables to describe the evolution of the rate-dependent phenomena. Based on this experimentally based motivation, an evolution equation using power laws is proposed to represent the effects of internal variables on viscosity phenomena. The proposed evolution equation has been incorporated in the finite strain viscoelasticity model in a thermodynamically consistent way.
Journal of Engineering Mechanics-asce, 2006
Rate-independent monotonic behavior of filled natural rubber and high damping rubber is investigated in compression and shear regimes. Monotonic responses obtained from tests conducted in both regimes demonstrate the prominent existence of the Fletcher-Gent effect, indicated by high stiffness at low strain levels. An improved hyperelasticity model for compression and shear regimes is proposed to represent the rate-independent instantaneous and equilibrium responses including the Fletcher-Gent effect. A parameter identification scheme involving simultaneous minimization of least-square residuals of uniaxial compression and simple shear data is delineated. The difficulties of identifying a unique set of hyperelasticity parameters that hold for both compression and shear deformation modes are thus overcome. The proposed hyperelasticity model has been implemented in a general purpose finite element program. Finite element simulations of experiments have shown the adequacy of the proposed hyperelasticity model, estimated parameters, and employed numerical procedures. Finally, numerical experiments were conducted to further explore the potential of the proposed model, and estimated parameters in analyzing rubber layers of a base isolation bearing subjected either to compression or to a combination of compression and shear.
CONSTITUTIVE MODELLING AND PARAMETER IDENTIFICATION FOR RUBBER-LIKE MATERIALS
The aim of the paper is to determine the phenomenological model to characterize the stress-strain relation and to simulate the behaviour of solid polyurethane (PUR) rubbers used in civil engineering, as well as to present the process of identification of model parameters for such materials. For the material studied the strain energy density function was established and a general constitutive relationship for the second-order tensor of Piola-Kirchhoff stress for elasticity is determined. Constitutive relationships for engineering stress in terms of the principal stretches are also specified. The paper presents the method of identification of parameters for constitutive models of hyperelasticity and hypoelasticity for the accessible experimental data. The applied identification procedure is based on the feature of two-phase structure of polyurethane material and is supported by the experimental data from uniaxial quasi-static tension and compression tests. In the analysis, the material behaviour was considered both for the case of incompressible deformation and also for the case of slightly compressible, nonlinearly elastic materials that are homogeneous and isotropic. The change of volume was admitted too, in range of large deformations in a tension and compression test. The attempt of description of stress-softening phenomenon was undertaken in rubber-like materials, for a given level of strain, under unloading (the Mullins effect) caused by the damage of microstructure of this material. Different descriptions of the stress-softening phenomenon were already proposed in the literature but they fail to give fully satisfactory conformity of experimental data with theoretical predictions. The phenomenological model by Elias-Zúñiga and Beatty, A new phenomenological model for stress-softening in elastomers, ZAMP, 53, 794-814, 2002, for such materials was modified by different softening functions and a simplified version of this model was identified, based on the experimental data. In the proposed model, the damage of microstructure was described by a new exponential function, which depends on the current magnitude of intensity of strain and its earlier maximum value during the process of material loading. In this paper, a suitable analysis of existent models and their verification based on experimental data for polyurethane rubber is presented for uniaxial experiments. It is shown that the magnitude of stress-softening varies with strain and this phenomenon increases with the magnitude of the pre-strain and the type of loading: monotonic tension, compression or cyclic loading. The obtained results are presented graphically for uniaxial tension and compression.
A hyperelastic constitutive model for rubber-like materials
European Journal of Mechanics - A/Solids, 2013
Hyperelastic behavior of isotropic incompressible rubbers is studied to develop a strain energy function which satisfies all the necessary characteristic properties of an efficient hyperelastic model. The proposed strain energy function includes only three material parameters which are somehow related to the physical quantities of the material molecular network. Moreover, the model benefits from mathematical simplicity, well suitting in all ranges of stretch and possessing the property of deformation-mode-independency. This reduces the required number of experimental tests for parameter calibration of the model. Results of the proposed model are compared with results of some available models as well as experimental data. Moreover, complete analysis of the Mooney plot over a wide range of stretch in extensionecompression is carried out. It is found that the proposed model gives reasonable predictions in comparison with those of experiments.
Constitutive modeling of rubberlike materials based on consistent strain energy density functions
2010
Rubberlike materials are characterized by high deformability and reversibility of deformation. From the continuum viewpoint, a strain energy density function is postulated for modeling the behavior of these materials. In this paper, a general form for the strain energy density of these materials is proposed from a phenomenological point of view. Based on the Valanis-Landel hypothesis, the strain energy density of incompressible materials is expressed as the sum of independent functions of the principal stretches meeting the essential requirements on the form of the strain energy density. It is cleared that the appropriate mathematical expressions for constitutive modeling of these materials are polynomial, logarithmic, and particularly exponential functions. In addition, the material parameters are calculated using a novel procedure that is based on the correlation between the values of the strain energy density (rather than the stresses) cast from the test data and the theory. In order to evaluate the performance of the proposed strain energy density functions, some test data of rubberlike materials with pure homogeneous deformations are used. It is shown that there is a good agreement between the test data and predictions of the models for incompressible isotropic materials.
The role of viscoelasticity in the mechanical modelling of rubbers
PROCEEDINGS OF THE 22ND INTERNATIONAL ESAFORM CONFERENCE ON MATERIAL FORMING: ESAFORM 2019
Bipolar plates (BPPs) are the main component in proton exchange membrane fuel cells. In the last years, different manufacturing processes have been proposed as alternative to the traditional graphite BPPs, including the manufacture of thin stamped BPPs using the rubber pad forming process. In this context, the numerical simulation of the forming process is used to optimize of the process parameters. Thus, in addition to the modelling of the elastoplastic behavior of the metallic sheet, it is also necessary to describe the hyper-viscoelastic behavior of the rubber pad. The main objective of this study is to evaluate the importance of the viscous effect on the global behavior of two different polyurethanes, since the modelling of the viscoelastic behavior is significantly more complex than the hyperelastic one. Uniaxial compression and stress relaxation tests are carried out both experimentally and numerically, considering three loading/unloading velocities. The hyperelastic behavior is described by the Mooney-Rivlin model, while the viscoelasticity is modelled by a series of Maxwell elements. The results show that the viscous effect can be neglected in the numerical modelling of the rubber pad forming, if the rubber hardness value is low.