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基于迭代法的非线性弹性均质化研究

侯淑娟 梁慧妍 汪全中 韩旭

侯淑娟, 梁慧妍, 汪全中, 韩旭. 基于迭代法的非线性弹性均质化研究[J]. 力学学报, 2018, 50(4): 837-846. doi: 10.6052/0459-1879-18-039
引用本文: 侯淑娟, 梁慧妍, 汪全中, 韩旭. 基于迭代法的非线性弹性均质化研究[J]. 力学学报, 2018, 50(4): 837-846. doi: 10.6052/0459-1879-18-039
Hou Shujuan, Liang Huiyan, Wang Quanzhong, Han Xu. STUDY ON NONLINEAR ELASTIC HOMOGENIZATION WITH ITERATIVE METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(4): 837-846. doi: 10.6052/0459-1879-18-039
Citation: Hou Shujuan, Liang Huiyan, Wang Quanzhong, Han Xu. STUDY ON NONLINEAR ELASTIC HOMOGENIZATION WITH ITERATIVE METHOD[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(4): 837-846. doi: 10.6052/0459-1879-18-039

基于迭代法的非线性弹性均质化研究

doi: 10.6052/0459-1879-18-039
基金项目: 国家自然科学基金(11572122)和汽车轻量化111创新引智基地(B16015)资助.
详细信息
    作者简介:

    *侯淑娟, 教授, 主要研究方向: 计算固体力学及其应用. E-mail:shujuanhou@hnu.edu.cn

    通讯作者:

    侯淑娟

  • 中图分类号: O343.5;

STUDY ON NONLINEAR ELASTIC HOMOGENIZATION WITH ITERATIVE METHOD

  • 摘要: 微观结构对复合材料的宏观力学性能具有至关重要的影响, 通过合理设计复合材料微观结构可以得到期望的宏观性能. 均质化方法作为一种有效的设计方法, 它从微观结构的角度出发, 利用均匀化的概念, 实现了对复合材料宏观力学性能的预测和设计. 而当考虑非线性因素, 均质化的实现就非常困难. 本文利用双渐近展开方法, 将位移按照宏观位移和微观位移展开, 推导了非线性弹性均质化方程. 通过直接迭代法, 对非线性弹性均质化方程进行了求解, 并给出了具体的迭代方法和实现步骤. 本文基于迭代步骤和非线性弹性均质化方程编写MATLAB 程序, 对3种典型本构关系的周期性多孔材料平面问题进行了计算, 对比细致模型的应变能、最大位移和等效泊松比, 对程序及迭代方法的准确性进行了验证. 之后对一种三元橡胶基复合材料进行多尺度均质化, 将其分为芯丝尺度和层间尺度. 用线弹性的均质化方法得到了芯丝尺度的等效弹性参数, 并将其作为层间尺度的材料参数. 在层间尺度应用非线性弹性均质化方法对结构进行计算, 得到材料的宏观等效性能, 并以实验结果为基准进行评价.

     

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  • 刊出日期:  2018-07-18

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