Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (2): 253-264.doi: https://doi.org/10.1007/s10483-016-2029-8

• 论文 • 上一篇    下一篇

Second-order two-scale computational method for ageing linear viscoelastic problem in composite materials with periodic structure

Yang ZHANG1, Junzhi CUI1,2, Yufeng NIE1   

  1. 1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China;
    2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
  • 收稿日期:2015-01-29 修回日期:2015-05-14 出版日期:2016-02-01 发布日期:2016-02-01
  • 通讯作者: Yufeng NIE E-mail:yfnie@nwpu.edu.cn
  • 基金资助:

    Project supported by the National Natural Science Foundation of China (No. 11471262)

Second-order two-scale computational method for ageing linear viscoelastic problem in composite materials with periodic structure

Yang ZHANG1, Junzhi CUI1,2, Yufeng NIE1   

  1. 1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072, China;
    2. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China
  • Received:2015-01-29 Revised:2015-05-14 Online:2016-02-01 Published:2016-02-01
  • Contact: Yufeng NIE E-mail:yfnie@nwpu.edu.cn
  • Supported by:

    Project supported by the National Natural Science Foundation of China (No. 11471262)

摘要:

The correspondence principle is an important mathematical technique to compute the non-ageing linear viscoelastic problem as it allows to take advantage of the computational methods originally developed for the elastic case. However, the correspon-dence principle becomes invalid when the materials exhibit ageing. To deal with this problem, a second-order two-scale (SOTS) computational method in the time domain is presented to predict the ageing linear viscoelastic performance of composite materials with a periodic structure. First, in the time domain, the SOTS formulation for calcu-lating the effective relaxation modulus and displacement approximate solutions of the ageing viscoelastic problem is formally derived. Error estimates of the displacement ap-proximate solutions for SOTS method are then given. Numerical results obtained by the SOTS method are shown and compared with those by the finite element method in a very fine mesh. Both the analytical and numerical results show that the SOTS computational method is feasible and efficient to predict the ageing linear viscoelastic performance of composite materials with a periodic structure.

关键词: ageing, composite material, periodic structure, second-order two-scale (SOTS) method, viscoelasticity

Abstract:

The correspondence principle is an important mathematical technique to compute the non-ageing linear viscoelastic problem as it allows to take advantage of the computational methods originally developed for the elastic case. However, the correspon-dence principle becomes invalid when the materials exhibit ageing. To deal with this problem, a second-order two-scale (SOTS) computational method in the time domain is presented to predict the ageing linear viscoelastic performance of composite materials with a periodic structure. First, in the time domain, the SOTS formulation for calcu-lating the effective relaxation modulus and displacement approximate solutions of the ageing viscoelastic problem is formally derived. Error estimates of the displacement ap-proximate solutions for SOTS method are then given. Numerical results obtained by the SOTS method are shown and compared with those by the finite element method in a very fine mesh. Both the analytical and numerical results show that the SOTS computational method is feasible and efficient to predict the ageing linear viscoelastic performance of composite materials with a periodic structure.

Key words: second-order two-scale (SOTS) method, ageing, composite material, periodic structure, viscoelasticity

中图分类号: 

APS Journals | CSTAM Journals | AMS Journals | EMS Journals | ASME Journals