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

doi:10.1007/s10483-016-2029-8

Abstract

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

2010 MSC Number:

Yang ZHANG, Junzhi CUI, Yufeng NIE. Second-order two-scale computational method for ageing linear viscoelastic problem in composite materials with periodic structure. Applied Mathematics and Mechanics (English Edition), 2016, 37(2): 253-264.

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