A fast multipole boundary element method for 2D viscoelastic problems |
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| Authors: | X.Y. Zhu W.Q. Chen Z.Y. Huang Y.J. Liu |
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| Affiliation: | 1. Department of Civil Engineering, Zhejiang University, Zijingang Campus, Hangzhou 310058, PR China;2. Department of Engineering Mechanics, Zhejiang University, Yuquan Campus, Hangzhou 310027, PR China;3. Department of Mechanical Engineering, University of Cincinnati, Cincinnati, OH 45221-0072, USA;4. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, PR China |
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| Abstract: | A fast multipole formulation for 2D linear viscoelastic problems is presented in this paper by incorporating the elastic–viscoelastic correspondence principle. Systems of multipole expansion equations are formed and solved analytically in Laplace transform domain. Three commonly used viscoelastic models are introduced to characterize the time-dependent behavior of the materials. Since the transformed multipole formulations are identical to those for the 2D elastic problems, it is quite easy to implement the 2D viscoelastic fast multipole boundary element method. Besides, all the integrals are evaluated analytically, leading to highly accurate results and fast convergence of the numerical scheme. Several numerical examples, including planar viscoelastic composites with single inclusion or randomly distributed multi-inclusions, as well as the problem of a crack in a pressured viscoelastic plane, are presented. The results are verified by comparison with the developed analytical solutions to illustrate the accuracy and efficiency of the approach. |
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