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An adaptive MsFEM for nonperiodic viscoelastic composites
Author(s) -
Klimczak Marek,
Cecot Witold
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5768
Subject(s) - microscale chemistry , finite element method , discretization , polygon mesh , viscoelasticity , nonlinear system , benchmark (surveying) , materials science , coupling (piping) , transient (computer programming) , computer science , mathematics , composite material , structural engineering , mathematical analysis , geometry , physics , engineering , mathematics education , geodesy , quantum mechanics , geography , operating system
Summary We present a modification of the multiscale finite element method (MsFEM) for modeling of heterogeneous viscoelastic materials and an enhancement of this method by the adaptive generation of both meshes, ie, a macroscale coarse one and a microscale fine one. The fine mesh refinements are performed independently within coarse elements adjusting the microscale discretization to the microstructure, whereas the coarse mesh adaptation optimizes the macroscale approximation. Besides the coupling of the hp ‐adaptive finite element method with the MsFEM we propose a modification of the MsFEM to accommodate for the analysis of transient nonlinear problems. We illustrate the efficiency and accuracy of the new approach for a number of benchmark examples, including the modeling of functionally graded material, and demonstrate the potential of our improvement for upscaling nonperiodic and nonlinear composites.