Analysis of the capabilities of the spectral element method in solving physically and geometrically nonlinear problems of mechanics using the CAE Fidesys package

Analysis of the capabilities of the spectral element method in solving physically and geometrically nonlinear problems of mechanics using the CAE Fidesys package

The article considers the problems of the formation of a neck in a sample of complex shape and Lüders slip bands in a square plate with a central circular hole in a plane-deformed state in finite deformations, taking into account the perfectly plastic flow. The statement of tasks is presented. Due t...

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Bibliographic Details
Published in:Continuum mechanics and thermodynamics Vol. 35; no. 4; pp. 1263 - 1273
Main Authors: Kozlov, V. V., Komolova, E. D., Kartsev, M. A., Filatova, A. V.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-07-2023
Springer
Springer Nature B.V
Subjects:
Charged particles
Classical and Continuum Physics
Deformation
Edge dislocations
Engineering Thermodynamics
Finite element analysis
Finite element method
Heat and Mass Transfer
Original Article
Physics
Physics and Astronomy
Plastic flow
Spectral element method
Square plates
Structural Materials
Theoretical and Applied Mechanics
Finite element method
Spectral element method
Geometric nonlinearity
Plasticity
Necking
Slip bands
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Summary:The article considers the problems of the formation of a neck in a sample of complex shape and Lüders slip bands in a square plate with a central circular hole in a plane-deformed state in finite deformations, taking into account the perfectly plastic flow. The statement of tasks is presented. Due to the symmetry, quarters of the models were considered. Numerical results were obtained in the CAE Fidesys package using the finite element method for the first and second orders, as well as for the spectral element method: for seven orders for the necking problem and the third-order elements for the Lüders slip bands problem. Based on the results obtained, the analysis of the capabilities of the spectral element method relative to the finite element method is carried out. The results of the conducted research can be useful when deciding on the use of the spectral element method in industrial problems.
ISSN:0935-1175
1432-0959
DOI:10.1007/s00161-022-01121-8