Comparison of elements and state-variable transfer methods for quasi-incompressible material behaviour in the particle finite element method

The Particle Finite Element Method (PFEM) is attractive for the simulation of large deformation problems, e.g. in free-surface fluid flows, fluid–structure interaction and in solid mechanics for geotechnical engineering and production processes. During cutting, forming or melting of metal, quasi-inc...

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Bibliographic Details
Published in:Computational mechanics Vol. 75; no. 2; pp. 755 - 773
Main Authors: Schewe, Markus, Bartel, Thorsten, Menzel, Andreas
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2025
Springer Nature B.V
Subjects:
Applied Mechanics
Classical and Continuum Physics
Computational Science and Engineering
Engineering
Engineering and Technology
Finite element analysis
Finite element method
Fluid flow
Fluid-structure interaction
Free surfaces
Geotechnical engineering
Incompressible flow
Maskinteknik
Mechanical Engineering
Original Paper
Plane strain
Poisson's ratio
Solid mechanics
State variable
Teknik
Teknisk mekanik
Theoretical and Applied Mechanics
Triangulation
Mapping of variables
Remeshing
Element technology
Numerical stability
Particle finite element method
ISSN:0178-7675, 1432-0924, 1432-0924
Online Access:Get full text
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Summary:The Particle Finite Element Method (PFEM) is attractive for the simulation of large deformation problems, e.g. in free-surface fluid flows, fluid–structure interaction and in solid mechanics for geotechnical engineering and production processes. During cutting, forming or melting of metal, quasi-incompressible material behaviour is often considered. To circumvent the associated volumetric locking in finite element simulations, different approaches have been proposed in the literature and a stabilised low-order mixed formulation (P1P1) is state-of-the-art. The present paper compares the established mixed formulation with a higher order pure displacement element (TRI6) under 2d plane strain conditions. The TRI6 element requires specialized handling, involving the deletion and re-addition of edge-mid-nodes during triangulation remeshing. The robustness of both element formulations is analysed along with different state-variable transfer schemes, which are not yet widely discussed in the literature. The influence of the stabilisation factor in the P1P1 element formulation is investigated, and an equation linking this factor to the Poisson ratio for hyperelastic materials is proposed.
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ISSN:0178-7675
1432-0924
1432-0924
DOI:10.1007/s00466-024-02531-y