考虑老化作用的废旧轮胎隔震垫的本构模型适用性及时变规律

doi:10.12068/j.issn.1005-3026.2025.20239062

摘要/Abstract

摘要：

目前诸多超弹性本构模型被广泛应用于橡胶隔震支座的有限元分析，而模型类别的选取以及对应参数的拟定则是关键.为研究不同品牌轮胎橡胶下的本构模型适用性以及老化后橡胶参数的变化规律，选择3种不同品牌的废旧轮胎进行单轴拉伸试验，同时选择一批轮胎进行77,154,231和308 h的热空气加速老化试验.根据拟定的模型参数用ABAQUS软件对废旧轮胎隔震垫(STP)进行建模与老化后支座竖向试验进行对比.结果表明：3种品牌轮胎橡胶应力应变曲线均呈现典型的反“S”形曲线，对比多种模型后确定Yeoh模型为最优.随老化时间增加，Yeoh模型参数近似呈现单调变化.老化前、后STP竖向刚度试验与有限元模拟值的误差均在可接受的范围内，验证了老化参数时变规律的准确性.本研究可以为废旧轮胎隔震支座以及其他废旧轮胎产品全寿命设计提供理论支撑.

关键词: Yeoh模型, 废旧轮胎隔震垫, 老化, 有限元分析

Abstract:

At present， many hyperelastic constitutive models are widely used in the finite element analysis of rubber isolation bearings. The selection of proper constitutive models and corresponding parameter determination are crucial in this process. This study aims to investigate the applicability of various hyperelastic constitutive models for different brands of tire rubber and the variation law of rubber parameters after aging. Three different brands of waste tires were selected for uniaxial tensile tests， while a batch of tires were selected for accelerated aging tests using hot air at 77， 154， 231， and 308 h. Employing the determined model parameters， the scrap tire rubber pads （STP） were modeled and compared with vertical experiments after aging using ABAQUS software. The results show that the stress-strain curves of the rubber in all three tire brands exhibit typical reverse “S” shapes， and the Yeoh model is determined to be optimal after comparing multiple models. The Yeoh model parameters approximately show monotonic changes with increasing aging time. The errors between the STP vertical stiffness test and the finite element simulation values before and after aging are within an acceptable range， which verifies the accuracy of the time-varying law of the aging parameters. This research provides theoretical support for the whole life design of STP and other waste tire products.

Key words: Yeoh model, scrap tire rubber pads, aging, finite element analysis

中图分类号:

TU 352.12

张广泰, 张军福, 陆东亮. 考虑老化作用的废旧轮胎隔震垫的本构模型适用性及时变规律[J]. 东北大学学报（自然科学版）, 2025, 46(5): 126-133.

Guang-tai ZHANG, Jun-fu ZHANG, Dong-liang LU. Applicability and Time Variation Law of Constitutive Model of Scrap Tire Rubber Pads Considering Aging Effect[J]. Journal of Northeastern University(Natural Science), 2025, 46(5): 126-133.

图/表 16

图1 哑铃试件拉伸前后对比

Fig.1 Comparison of dumbbell specimens before and after stretching

表1 橡胶本构函数类型

Table 1 Constitutive function type of rubber

本构函数	应变能函数形式	工程应力与伸长率的关系
Neo-Hookean	$W = C 10 I 1 - 3$	$σ = 2 C 10 λ - λ - 2$
Mooney-Rivlin	$W = C 10 I 1 - 3 + C 01 I 2 - 3 + 1 D 1 J - 1 2$	$σ = 2 C 10 λ - λ - 2 + 2 C 01 （ 1 - λ - 3 ）$
Yeoh	$W = C 10 I 1 - 3 + C 20 I 1 - 3 2 + C 30 I 1 - 3 3$	$σ = ∑ i = 1 N 2 i C i 0 λ 2 + 2 λ - 1 - 3 i - 1 （ λ - λ - 2 ）$
Ogden	$W = ∑ i = 1 N μ i α i λ 1 α i + λ 2 α i + λ 3 α i - 3$	$σ = ∑ i = 1 N μ i λ α i - 1 + λ - 12 α i - 1$

表1 橡胶本构函数类型

Table 1 Constitutive function type of rubber

本构函数	应变能函数形式	工程应力与伸长率的关系
Neo-Hookean	$W = C 10 I 1 - 3$	$σ = 2 C 10 λ - λ - 2$
Mooney-Rivlin	$W = C 10 I 1 - 3 + C 01 I 2 - 3 + 1 D 1 J - 1 2$	$σ = 2 C 10 λ - λ - 2 + 2 C 01 （ 1 - λ - 3 ）$
Yeoh	$W = C 10 I 1 - 3 + C 20 I 1 - 3 2 + C 30 I 1 - 3 3$	$σ = ∑ i = 1 N 2 i C i 0 λ 2 + 2 λ - 1 - 3 i - 1 （ λ - λ - 2 ）$
Ogden	$W = ∑ i = 1 N μ i α i λ 1 α i + λ 2 α i + λ 3 α i - 3$	$σ = ∑ i = 1 N μ i λ α i - 1 + λ - 12 α i - 1$

图2 3种品牌橡胶应力应变关系

Fig.2 Stress-strain relationships for three brands of rubber

表2 普利司通轮胎超弹性本构参数及拟合误差

Table 2 Hyperelastic constitutive parameters and fitting errors of Bridgestone tires

C₁₀=1.469

C₁₀=2.775，C₀₁=-3.42

C₁₀=0.623 9，C₂₀=0.096 81

C₃₀=-0.001 968

μ 1 = 0.692 5, α 1 = 3.385

R²

表2 普利司通轮胎超弹性本构参数及拟合误差

Table 2 Hyperelastic constitutive parameters and fitting errors of Bridgestone tires

模型

Neo-Hookean

Mooney-Rivlin

Yeoh

Ogden

参数

C₁₀=1.469

C₁₀=2.775，C₀₁=-3.42

C₁₀=0.623 9，C₂₀=0.096 81

C₃₀=-0.001 968

μ 1 = 0.692 5, α 1 = 3.385

R²

0.842 4

0.978 1

0.998 3

0.997 5

表3 邓禄普轮胎超弹性本构参数及误差

Table 3 Hyperelastic constitutive parameters and fitting errors of Dunlop tires

C₁₀=1.357

C₁₀=2.547，C₀₁=-2.706

C₁₀=0.828 3，C₂₀=0.050 06

C₃₀=0.004 193

μ 1 = 0.676 5, α 1 = 3.535

R²

表3 邓禄普轮胎超弹性本构参数及误差

Table 3 Hyperelastic constitutive parameters and fitting errors of Dunlop tires

模型

Neo-Hookean

Mooney-Rivlin

Yeoh

Ogden

参数

C₁₀=1.357

C₁₀=2.547，C₀₁=-2.706

C₁₀=0.828 3，C₂₀=0.050 06

C₃₀=0.004 193

μ 1 = 0.676 5, α 1 = 3.535

R²

0.860 5

0.965 3

0.997 3

0.993 4

表4 米其林轮胎超弹性本构参数及误差

Table 4 Hyperelastic constitutive parameters and fitting errors of Michelin tires

C₁₀=1.26

C₁₀=2.13，C₀₁=-2.529

C₁₀=0.607 5，C₂₀=0.059 65

C₃₀=-0.001 166

μ 1 = 0.748 3, α 1 = 3.057

R²

表4 米其林轮胎超弹性本构参数及误差

Table 4 Hyperelastic constitutive parameters and fitting errors of Michelin tires

模型

Neo-Hookean

Mooney-Rivlin

Yeoh

Ogden

参数

C₁₀=1.26

C₁₀=2.13，C₀₁=-2.529

C₁₀=0.607 5，C₂₀=0.059 65

C₃₀=-0.001 166

μ 1 = 0.748 3, α 1 = 3.057

R²

0.880 6

0.987 9

0.999 7

0.993 4

图3 不同超弹性模型和试验数据对比（a）—邓禄普；（b）—普利司通；（c）—米其林.

Fig.3 Comparison of different hyperelastic models and test data

图4 邓禄普轮胎老化0~100 a应力应变关系

Fig.4 Stress-strain relationship of Dunlop tires aging 0~100 years

表5 老化后邓禄普轮胎超弹性本构参数

Table 5 Hyperelastic constitutive parameters of aged Dunlop tires

时间/a	0	25	50	75	100
C₁₀	0.757 5	0.687 8	0.657 4	0.557 9	0.501 4
C₂₀	0.115 40	0.109 30	0.078 34	0.069 45	0.065 04
C₃₀	-0.001 764	-0.001 933	-0.001 637	-0.001 504	-0.001 097
R²	0.997 1	0.999 4	0.999 8	0.999 8	0.999 4

图5 2型哑铃试件建模图

Fig.5 Modelling diagram of type 2 dumbbell specimen

图6 C10递减对应的应力应变关系

Fig.6 Corresponding stress-strain relationship with decreasing C10

图7 C20递减对应的应力应变关系

Fig.7 Corresponding stress-strain relationship with decreasing C20

图8 C30递减对应的应力应变关系

Fig.8 Corresponding stress-strain relationship with decreasing C30

图9 Yeoh本构参数随时间变化拟合对比

Fig.9 Comparison of Yeoh constitutive parameters fitting with time

图10 废旧轮胎隔震垫建模图

Fig.10 Scrap tire rubber pads modelling diagram

图11 6 MPa下竖向刚度试验值与模拟值

Fig.11 Test and simulation values of vertical stiffness at 6 MPa

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