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

Abstract

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.

Soft, Tough, and Thermally Conductive Elastomer Composites by Constructing a Curled Conformation

“…We used finite element simulation for characteristic tensile behavior of the C-PDMS/60 wt % BN and the E-PDMS/60 wt % BN to intuitively understand the softness, toughness, and stretchability brought about by the curled conformation. First, the stress−strain curves of C-PDMS/60 wt % BN and E-PDMS/ 60 wt % BN are used as the parameter source, and the Ogden hyperelastic constitutive model equation is used for fitting: 34,35…”

“…We used finite element simulation for characteristic tensile behavior of the C-PDMS/60 wt % BN and the E-PDMS/60 wt % BN to intuitively understand the softness, toughness, and stretchability brought about by the curled conformation. First, the stress–strain curves of C-PDMS/60 wt % BN and E-PDMS/60 wt % BN are used as the parameter source, and the Ogden hyperelastic constitutive model equation is used for fitting: , P O g d e n S T = prefix∑ i = 1 N μ i S T false( λ α i S T − 1 − λ − false( 1 / 2 false) α i S T − 1 false) where μ i and α i are the fitting parameters, which is summarized in Table S3, and the fitting curves of the C-PDMS/60 wt % BN and E-PDMS/60 wt % BN are shown in Figure S16. We used this constitutive model to represent the mechanical behavior of the C-PDMS/60 wt % BN and E-PDMS/60 wt % BN in FEA.…”

Research and Development of High-Performance High-Damping Rubber Materials for High-Damping Rubber Isolation Bearings: A Review

“…Based on the experimental results, an Arruda-Boyce model (eight-chain model) containing explicit temperature-dependent parameters was proposed. The comparison between the experimental and the numerical results showed that the model was able to estimate well the hyperelastic behavior of the rubber material in the strain range of 0-150% within the temperature range of 20-110 • C. On this basis, in [114], an exponential correction term was introduced to the Arruda-Boyce model and a modified Arruda-Boyce model was proposed to further consider the interaction effect between different components in the material. By comparing the ability of different models of the rubber material (Neo-Hookean [99], Mooney-Rivlin [98,100], Ogden [101], and Yeoh [103] models) in the prediction of experimental results, it showed that the proposed modified Arruda-Boyce model could more accurately estimate the static mechanical properties of carbon black filled natural rubber materials.…”

Systematic Fitting and Comparison of Hyperelastic Continuum Models for Elastomers

“…Treloar & Kawabata data Compiling rankings, discussing alternative cost functions with weights for each experiment, presenting a generic fitting algorithm, discussing predictivity to other deformation modes [30] 7 2 CB-filled, S-crosslinked NRs Proposing a new model, analyzing temperature dependencies [41] 75 Treloar data & CB-filled HNBR from [45] Compiling top ten rankings, comparing run time of finite element simulations Table 2 Review articles on volumetric hyperelastic models (n is the number of models; CB: carbon black, EPDM: ethylene propylene diene rubber, S: sulfur) Literature n Experimental data Objective [66] 5 None Discussing constraints on volumetric strain energy functions [26] 5 None Discussing constraints on volumetric strain energy functions, proposing new models [38] 10 None Discussing polyconvexity (also for isochoric models), proposing new models [83] 4 CB-filled, S-crosslinked EPDM Illustrating the effect of CB content, crosslink content and curing time on the bulk modulus reasonable constraints on the parameter bounds are recapped and crucial model properties are highlighted. Another difference between the present work and existing contributions is that the treatment of the experimental data is highlighted.…”

“…2 with a maximum uniaxial stress of 6.6 MPa and a maximum equibiaxial stress of 2.5 MPa . In addition, the relative error in residual (30) gives a higher weight to the range of low stresses than the (28)…”