Hyper-Pseudo-Viscoelastic Model and Parameter Identification for Describing Tensile Recovery Stress–Strain Responses of Rubber Components in TBR
Abstract
:1. Introduction
2. Flow Chart of Numerical Calculation of Tensile Recovery Stress–Strain Responses
3. Experiments and Data Adjustment
3.1. Material Preparation
3.2. Quasi-Static Cyclic Stretching Experiments
3.3. Experimental Data Adjustment
4. Constitutive Models for Rubber Material
4.1. Hyperelastic Constitutive Model
4.2. The Ogden–Roxburgh Pseudoelastic Model
4.3. Viscoelastic Constitutive Model
5. Results and Discussion
5.1. Parameter Identification
5.2. Finite Element Analysis of the Tensile Recovery of Dumbbell-Shaped Specimen
6. Conclusions
- Nine rubber materials used in different components of TBR tires were subjected to tensile recovery experiments with different peak strain levels. An experimental data processing method was proposed to facilitate the parameter identification for the hyper-pseudo-viscoelastic model. The workflow of how to perform numerical calculation of tensile recovery stress–strain responses of rubber materials in tires was described.
- The Yeoh hyperelastic model, the Ogden–Roxburgh pseudoelastic model and the Prony series viscoelastic model were adopted together to describe the tensile recovery mechanical responses (loading curve, unloading curve and permanent set) of nine different rubber materials. The fitting result data are all in good agreement with the adjusted test data, and all the coefficients of determination exceeded 0.975. This method has certain universality.
- This study indicates that using the hyper-pseudo-viscoelastic constitutive model to predict the quasi-static cyclic loading of rubber materials is a feasible method. This work can guide the mechanical research of soft substances and rubber-like materials, and provides a support to design high-durability rubber products and high-performance tires.
- However, the introduction of complex nonlinear constitutive equations usually makes the finite element analysis have great convergence problems. In this work, the hyper-pseudo-viscoelastic constitutive model is only used for the deformation analysis of a simple dumbbell-shaped rubber specimen. For more complex products such as tires, the applicability of these models needs to be further explored.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Yeoh Hyperelastic Model | Ogden-Roxburgh Pseudoelastic Model | Prony Series Viscoelastic Model | |||||
---|---|---|---|---|---|---|---|
C10 | 1.2286 | r | 1.5022 | G1 | 0.20 | τ1 | 0.1 |
G2 | 0.15 | τ2 | 1.0 | ||||
C20 | 0.0055 | m | 1.3038 | ||||
G3 | 0.08 | τ3 | 10.0 | ||||
C30 | 0.0007 | β | 0.0605 | ||||
G4 | 0.05 | τ4 | 100.0 |
Yeoh Hyperelastic Model | Ogden–Roxburgh Pseudoelastic Model | Prony Series Viscoelastic Model | |||||
---|---|---|---|---|---|---|---|
C10 | 0.9750 | r | 1.7874 | G1 | 0.0303 | τ1 | 0.1 |
G2 | 0.3588 | τ2 | 1.0 | ||||
C20 | 0.0156 | m | 0.7440 | ||||
G3 | 0.0742 | τ3 | 10.0 | ||||
C30 | 0.0001 | β | 0.0331 | ||||
G4 | 0.0641 | τ4 | 100.0 |
The Peak Strain Level | Permanent Set of the Adjusted Test Data | Permanent Set of the Fitting Data | Relative Error |
---|---|---|---|
20% | 0.033 | 0.037 | 12.1% |
40% | 0.066 | 0.069 | 4.5% |
80% | 0.143 | 0.150 | 4.9% |
120% | 0.224 | 0.231 | 3.1% |
200% | 0.387 | 0.392 | 1.3% |
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Pan, G.; Chen, M.; Wang, Y.; Zhang, J.; Liu, L.; Zhang, L.; Li, F. Hyper-Pseudo-Viscoelastic Model and Parameter Identification for Describing Tensile Recovery Stress–Strain Responses of Rubber Components in TBR. Polymers 2023, 15, 76. https://doi.org/10.3390/polym15010076
Pan G, Chen M, Wang Y, Zhang J, Liu L, Zhang L, Li F. Hyper-Pseudo-Viscoelastic Model and Parameter Identification for Describing Tensile Recovery Stress–Strain Responses of Rubber Components in TBR. Polymers. 2023; 15(1):76. https://doi.org/10.3390/polym15010076
Chicago/Turabian StylePan, Gao, Meimei Chen, Yao Wang, Jichuan Zhang, Li Liu, Liqun Zhang, and Fanzhu Li. 2023. "Hyper-Pseudo-Viscoelastic Model and Parameter Identification for Describing Tensile Recovery Stress–Strain Responses of Rubber Components in TBR" Polymers 15, no. 1: 76. https://doi.org/10.3390/polym15010076