Polygonal finite element modeling of crack propagation via automatic adaptive mesh refinement

Maryam Shahrezaei | Hamid Moslemi

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URL :   http://research.shahed.ac.ir/WSR/WebPages/Report/PaperView.aspx?PaperID=137815
Date :  2020/09/25
Publish in :    Structural Engineering and Mechanics
DOI :  https://doi.org/10.12989/sem.2020.75.6.685
Link :  http://www.techno-press.org/content/?page=article&journal=sem&volume=75&num=6&ordernum=4
Keywords :polygonal finite element; adaptive mesh refinement; error estimation; crack propagation; linear fracture mechanics

Abstract :

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Polygonal finite element provides a great flexibility in mesh generation of crack propagation problems where the topology of the domain changes significantly. However, the control of the discretization error in such problems is a main concern. In this paper, a polygonal-FEM is presented in modeling of crack propagation problems via an automatic adaptive mesh refinement procedure. The adaptive mesh refinement is accomplished based on the Zienkiewicz–Zhu error estimator in conjunction with a weighted SPR technique. Adaptive mesh refinement is employed in some steps for reduction of the discretization error and not for tracking the crack. In the steps that no adaptive mesh refinement is required, local modifications are applied on the mesh to prevent poor polygonal element shapes. Finally, several numerical examples are analyzed to demonstrate the efficiency, accuracy and robustness of the proposed computational algorithm in crack propagation problems.