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

作　　者：Yang ZHANG Junzhi CUI Yufeng NIE 

机构地区：[1]Department of Applied Mathematics, Northwestern Polytechnical University [2]Academy of Mathematics and Systems Science, Chinese Academy of Sciences

出　　处：《Applied Mathematics and Mechanics(English Edition)》2016年第2期253-264,共12页应用数学和力学（英文版）

基　　金：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.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：second-order two-scale （SOTS） method ageing VISCOELASTICITY composite material periodic structure 

分 类 号：O344[理学—固体力学]