Numerical Analysis of Benchmark Finite Strain Plasticity Problems using High-order Finite Elements and Finite Cells

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TAGHIPOUR A.A.; PARVIZIAN J.; Heinze S.; Duster A.; Rank e.

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Journal: JOURNAL OF COMPUTATIONAL METHODS IN ENGINEERING (ESTEGHLAL) Year:2018 | Volume:37 | Issue:1 Page(s): 11-28

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Title

Numerical Analysis of Benchmark Finite Strain Plasticity Problems using High-order Finite Elements and Finite Cells

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Keywords

High-order finite element methodQ1

Finite cell methodQ1

Finite strain plasticityQ1

IncompressibilityQ1

Volumetric lockingQ1

Abstract

In this paper, a high-order finite element discretization and its newly developed fictitious domain approach, the Finite cell method, are employed to compute a series of benchmark problems in the finite strain von Mises or J2 theory of plasticity. The hierarchical (integrated Legendre) shape functions are used for the finite element approximation of incompressible plastic dominated deformations occurring in the Finite strain plasticity of ductile metals. The computational examples include the necking under uniaxial tension with notched and un-notched samples and the compression of a perforated plate. These computations demonstrate that the High-order finite element methods can provide a locking-free behavior with a pure displacement-based formulation. They also provide high convergence rates and robustness against high mesh distortions. In addition, it is shown that the Finite cell method, on the top of the aforementioned advantages, provides easy mesh generation capabilities for highly complex geometries. The computational results are verified in comparison with the results obtained using a standard low-order finite element method known as the F-bar method. The numerical investigations reveal that both methods are good candidates for the plasticity analysis of engineering materials and structures made up of ductile materials, particularly those involving complex geometries.

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APA: Copy

TAGHIPOUR, A.A., PARVIZIAN, J., Heinze, S., Duster, A., & Rank, e.. (2018). Numerical Analysis of Benchmark Finite Strain Plasticity Problems using High-order Finite Elements and Finite Cells. JOURNAL OF COMPUTATIONAL METHODS IN ENGINEERING (ESTEGHLAL), 37(1 ), 11-28. SID. https://sid.ir/paper/173647/en

Vancouver: Copy

TAGHIPOUR A.A., PARVIZIAN J., Heinze S., Duster A., Rank e.. Numerical Analysis of Benchmark Finite Strain Plasticity Problems using High-order Finite Elements and Finite Cells. JOURNAL OF COMPUTATIONAL METHODS IN ENGINEERING (ESTEGHLAL)[Internet]. 2018;37(1 ):11-28. Available from: https://sid.ir/paper/173647/en

IEEE: Copy

A.A. TAGHIPOUR, J. PARVIZIAN, S. Heinze, A. Duster, and e. Rank, “Numerical Analysis of Benchmark Finite Strain Plasticity Problems using High-order Finite Elements and Finite Cells,” JOURNAL OF COMPUTATIONAL METHODS IN ENGINEERING (ESTEGHLAL), vol. 37, no. 1 , pp. 11–28, 2018, [Online]. Available: https://sid.ir/paper/173647/en

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