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考虑缠结效应的超弹性本构模型

肖锐 向玉海 钟旦明 曲绍兴

肖锐, 向玉海, 钟旦明, 曲绍兴. 考虑缠结效应的超弹性本构模型[J]. 力学学报, 2021, 53(4): 1028-1037. doi: 10.6052/0459-1879-21-008
引用本文: 肖锐, 向玉海, 钟旦明, 曲绍兴. 考虑缠结效应的超弹性本构模型[J]. 力学学报, 2021, 53(4): 1028-1037. doi: 10.6052/0459-1879-21-008
Xiao Rui, Xiang Yuhai, Zhong Danming, Qu Shaoxing. HYPERELASTIC MODEL WITH ENTANGLEMENT EFFECT[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(4): 1028-1037. doi: 10.6052/0459-1879-21-008
Citation: Xiao Rui, Xiang Yuhai, Zhong Danming, Qu Shaoxing. HYPERELASTIC MODEL WITH ENTANGLEMENT EFFECT[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(4): 1028-1037. doi: 10.6052/0459-1879-21-008

考虑缠结效应的超弹性本构模型

doi: 10.6052/0459-1879-21-008
基金项目: 1)国家自然科学基金(12022204);国家自然科学基金(11872170);国家自然科学基金(91748209)
详细信息
    作者简介:

    3)曲绍兴, 教授, 主要研究方向: 智能软材料和软机器. E-mail: squ@zju.edu.cn
    2)肖锐, 研究员, 主要研究方向: 软材料本构关系. E-mail: rxiao@zju.edu.cn;

    通讯作者:

    肖锐

    曲绍兴

  • 中图分类号: O341

HYPERELASTIC MODEL WITH ENTANGLEMENT EFFECT

  • 摘要: 经典熵弹性模型, 如 Neo-Hookean模型和Arruda-Boyce八链模型, 被广泛应用于预测橡胶等软材料的超弹性力学行为. 然而, 大量实验结果也显示仅采用一套模型参数, 这类模型不能同时准确地描述橡胶在多种加载模式下的应力响应. 为了克服上述模型的不足, 本文在熵弹性的模型基础上引入缠结约束效应. 微观上, 采用Langevin统计模型来表征熵弹性变形自由能, 通过管模型(tube model)引入缠结约束自由能, 并基于仿射假设, 建立微观变形与宏观变形之间的映射关系. 在宏观上, 所建立的超弹性模型的Helmholtz自由能同时包含熵弹性和缠结约束两部分, 其中熵弹性自由能与经典的Arruda-Boyce八链模型一致, 依赖于柯西-格林应变张量的第一不变量, 而缠结约束自由能依赖于柯西-格林应变张量的第二不变量. 与文献中的实验结果对比发现, 该三参数模型能准确地预测实验中所测得的橡胶材料在单轴拉伸、纯剪切和等双轴拉伸变形条件下的应力响应, 也能较好地描述不同预拉伸比条件下双轴拉伸实验结果. 最后, 本文比较了所建立的基于应变不变量的缠结约束模型与文献中相关的缠结约束模型在多种加载模式下自由能的异同. 总的来说, 本文所建立的本构理论能准确模拟橡胶等软材料的大变形力学行为, 对其工程应用有促进作用.

     

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出版历程
  • 收稿日期:  2021-01-06
  • 刊出日期:  2021-04-10

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