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基于Treloar实验数据的超弹性材料完全本构关系研究

韩磊 王新彤 李录贤

韩磊, 王新彤, 李录贤. 基于Treloar实验数据的超弹性材料完全本构关系研究. 力学学报, 2022, 54(12): 1-12 doi: 10.6052/0459-1879-22-317
引用本文: 韩磊, 王新彤, 李录贤. 基于Treloar实验数据的超弹性材料完全本构关系研究. 力学学报, 2022, 54(12): 1-12 doi: 10.6052/0459-1879-22-317
Han Lei, Wang Xintong, Li Luxian. Complete constitutive relation of hyperelastic materials for Treloar’s experimental data. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 1-12 doi: 10.6052/0459-1879-22-317
Citation: Han Lei, Wang Xintong, Li Luxian. Complete constitutive relation of hyperelastic materials for Treloar’s experimental data. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(12): 1-12 doi: 10.6052/0459-1879-22-317

基于Treloar实验数据的超弹性材料完全本构关系研究

doi: 10.6052/0459-1879-22-317
基金项目: 国家自然科学基金资助项目(U20B2013)
详细信息
    作者简介:

    李录贤, 教授, 主要研究方向: 固体力学的基本理论、新型材料的力学行为及新型数值方法. E-mail: luxianli@mail.xjtu.edu.cn

  • 中图分类号: O34

COMPLETE CONSTITUTIVE RELATION OF HYPERELASTIC MATERIALS FOR TRELOAR’S EXPERIMENTAL DATA

  • 摘要: 超弹性材料在航天航空、民用工业等多个领域已得到广泛应用, 但因具有的大变形非线性特性, 其本构行为异常复杂, 本构模型多种多样. 本文从超弹性材料的应变能函数出发, 在连续介质力学框内开展超弹性材料完全本构关系的理论与应用研究. 首先, 分析了Treloar针对某硫化橡胶超弹性材料开展的单轴拉伸、等双轴拉伸以及纯剪切3种基本变形模式实验数据的特点; 接着, 理论分析了这3种变形模式所具有的相同应力条件, 从而将3种模式的本构关系均表示为加载方向应力随伸长比的变化, 并就$I_1^m$$I_2^m$两类幂函数型应变能函数的本构特性进行了研究; 然后, 将实验曲线分为初始和剩余两个阶段, 对初始阶段采用neo-Hookean模型应变能函数、对剩余阶段采用非指定指数的幂函数型应变能函数, 在3种变形模式实验数据总体误差泛函最小条件下对模型参数进行识别, 最终建立了典型超弹性材料的完全本构关系. 对3种基本变形模式下的不同响应进行了重新预测, 其结果均优于文献上已发表的多个本构模型. 本文工作表明, 依据多种不同变形模式下全程变形范围的实验曲线, 可建立超弹性材料的完全本构关系, 从而为超弹性材料断裂等复杂问题的理论研究与实际应用提供支撑.

     

  • 图  1  ST, ET和PS实验数据汇总

    Figure  1.  Collection of experimental data under ST, ET and PS states

    图  2  纯剪试件示意图

    Figure  2.  Schematic of pure shear specimen

    图  3  典型m取值时$ {W_1} = {I_1}^m $对3种变形模式的本构描述

    Figure  3.  Constitutive behavior of three deformation modes described by $ {W_1} = {I_1}^m $ for typical values of m

    图  4  典型m取值时$ {W_2} = {I_2}^m $所表征的三种变形模式本构特性

    Figure  4.  Constitutive behavior of three deformation modes described by $ {W_2} = {I_2}^m $ for typical values of m

    图  5  3种变形模式的更新实验数据

    Figure  5.  Updated experimental data of three deformation modes

    图  6  对3种变形模式更新实验数据的预测效果

    Figure  6.  Predicted effect for the updated experimental data of three deformation modes

    图  7  完全本构关系对3种不同模式实验曲线的预测效果

    Figure  7.  Predicted effect of complete constitutive relation for the three different modes

    图  9  Mansouri模型对不同变形模式实验数据的预测效果

    Figure  9.  Predicted effect of the Mansouri model for experimental data of different deformation modes

    9  Mansouri模型对不同变形模式实验数据的预测效果(续)

    9.  Predicted effect of the Mansouri model for experimental data of different deformation modes (continued)

    表  1  单轴拉伸变形模式的实验数据

    Table  1.   Experimental data of the ST deformation mode

    No.Stretch
    ratio $\lambda $
    Engineering
    stress T/MPa
    No.Stretch
    ratio $\lambda $
    Engineering
    stress T/MPa
    11.020.0255135.361.9502
    21.120.1343145.752.3128
    31.240.2254156.152.6852
    41.390.3165166.43.0380
    51.580.4077176.63.4104
    61.900.4998186.853.7730
    72.180.5880197.054.1258
    82.420.6762207.154.4884
    93.020.8624217.254.8608
    103.571.0486227.45.2234
    114.031.2250237.55.5860
    124.761.5876247.66.3112
    下载: 导出CSV

    表  3  纯剪切变形模式的实验数据

    Table  3.   Experimental data of the PS deformation mode

    No.Stretch
    ratio
    $\lambda $
    Engineering
    stress T/MPa
    No.Stretch
    ratio
    $\lambda $
    Engineering
    stress T/MPa
    11.000.0082.400.76
    21.060.0792.980.93
    31.140.16103.481.11
    41.210.24113.961.28
    51.320.33124.361.46
    61.460.42134.691.62
    71.870.59144.961.79
    下载: 导出CSV

    表  2  等双轴拉伸变形模式的实验数据

    Table  2.   Experimental data of the ET deformation mode

    No.Stretch
    ratio
    $\lambda $
    Engineering
    stress T/MPa
    No.Stretch
    ratio
    $\lambda $
    Engineering
    stress T/MPa
    11.000.00101.940.77
    21.040.09112.490.96
    31.080.16123.031.24
    41.120.24133.431.45
    51.140.26143.751.72
    61.200.33154.031.96
    71.310.44164.262.22
    81.420.51174.442.43
    91.690.65
    下载: 导出CSV

    表  4  初始阶段数据及其对应变形模式

    Table  4.   Data in the initial regime and the associated deformation modes

    No.Deformation modeStretch ratio $\lambda $Engineering stress T/MPa
    1ST1.020.0255
    2ET1.040.09
    3PS1.060.07
    4ET1.080.16
    5ST1.120.1343
    6ET1.120.24
    下载: 导出CSV

    表  5  不同本构模型的预测精度比较

    Table  5.   Comparison of prediction accuracy of different constitutive models

    Strain energy functionOverall error functional
    STETPSOverall
    Eq. (19)[26]0.21360.029250.018100.2609
    Eq. (17) 0.13710.018240.0078110.1632
    Eq. (22) 0.14880.013510.0071240.1694
    下载: 导出CSV

    1  单轴拉伸实验数据

    1.   Experimental data under the ST state

    No.Stretch ratio$\lambda $Engineering stress T/MPaNo.Stretch ratio$\lambda $Engineering stress T/MPa
    11.0520.074112.2990.688
    21.1160.134122.5020.749
    31.1910.198132.6850.809
    41.2670.259142.8730.870
    51.3630.319153.0520.933
    61.4740.383163.2230.994
    71.6100.443173.3821.058
    81.7650.504183.5221.115
    91.9360.564193.6771.178
    102.1160.624
    下载: 导出CSV

    2  纯剪切实验数据

    2.   Experimental under the PS state

    No.Stretch ratio$\lambda $Engineering stress T/MPaNo.Stretch ratio$\lambda $Engineering stress T/MPa
    11.0470.068121.9961.147
    21.0970.114132.0981.291
    31.1490.152142.1971.443
    41.1990.205152.2971.618
    51.2980.304162.3961.777
    61.3970.418172.4951.952
    71.4970.524182.5952.127
    81.5960.638192.6972.301
    91.6980.752202.7962.484
    101.7970.873212.8462.582
    111.8971.010
    下载: 导出CSV
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出版历程
  • 收稿日期:  2022-07-10
  • 录用日期:  2022-10-27
  • 网络出版日期:  2022-10-28

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