Open Access

ARTICLE

Development of a Three-Dimensional Multiscale Octree SBFEM for Viscoelastic Problems of Heterogeneous Materials

Xu Xu¹, Xiaoteng Wang¹, Haitian Yang¹, Zhenjun Yang², Yiqian He^1,3,*

1 State Key Laboratory of Structural Analysis, Optimization and CAE Software for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116024, China
2 Hubei Key Laboratory of Geotechnical and Structural Safety, School of Civil Engineering, Wuhan University, Wuhan, 430072, China
3 Mechanik–Materialtheorie, Ruhr-Universität Bochum, Bochum, 44801, Germany

* Corresponding Author: Yiqian He. Email:

(This article belongs to the Special Issue: Advances on Mesh and Dimension Reduction Methods)

Computer Modeling in Engineering & Sciences 2024, 140(2), 1831-1861. https://doi.org/10.32604/cmes.2024.048199

Received 30 November 2023; Accepted 06 March 2024; Issue published 20 May 2024

Abstract

The multiscale method provides an effective approach for the numerical analysis of heterogeneous viscoelastic materials by reducing the degree of freedoms (DOFs). A basic framework of the Multiscale Scaled Boundary Finite Element Method (MsSBFEM) was presented in our previous works, but those works only addressed two-dimensional problems. In order to solve more realistic problems, a three-dimensional MsSBFEM is further developed in this article. In the proposed method, the octree SBFEM is used to deal with the three-dimensional calculation for numerical base functions to bridge small and large scales, the three-dimensional image-based analysis can be conveniently conducted in small-scale and coarse nodes can be flexibly adjusted to improve the computational accuracy. Besides, the Temporally Piecewise Adaptive Algorithm (TPAA) is used to maintain the computational accuracy of multiscale analysis by adaptive calculation in time domain. The results of numerical examples show that the proposed method can significantly reduce the DOFs for three-dimensional viscoelastic analysis with good accuracy. For instance, the DOFs can be reduced by 9021 times compared with Direct Numerical Simulation (DNS) with an average error of 1.87% in the third example, and it is very effective in dealing with three-dimensional complex microstructures directly based on images without any geometric modelling process.

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Keywords

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