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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Veröffentlicht in:	Computational mechanics Jg. 75; H. 2; S. 755 - 773
Hauptverfasser:	Schewe, Markus, Bartel, Thorsten, Menzel, Andreas
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2025 Springer Nature B.V
Schlagworte:	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
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Abstract	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.
AbstractList	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. 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. 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 influenceof 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.
Author	Bartel, Thorsten Menzel, Andreas Schewe, Markus
Author_xml	– sequence: 1 givenname: Markus orcidid: 0000-0003-4180-0760 surname: Schewe fullname: Schewe, Markus email: markus.schewe@tu-dortmund.de organization: Institute of Mechanics, TU Dortmund – sequence: 2 givenname: Thorsten orcidid: 0000-0002-7953-8342 surname: Bartel fullname: Bartel, Thorsten organization: Institute of Mechanics, TU Dortmund – sequence: 3 givenname: Andreas orcidid: 0000-0002-7819-9254 surname: Menzel fullname: Menzel, Andreas organization: Institute of Mechanics, TU Dortmund, Division of Solid Mechanics, Lund University
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Cites_doi	10.1016/j.jrmge.2021.12.006 10.1016/j.compstruc.2011.07.004 10.1115/1.4034434 10.1137/S0036142905444482 10.1007/s40571-016-0145-0 10.1016/j.compgeo.2020.103994 10.1007/s00466-014-1088-z 10.1002/nme.5962 10.1007/s00466-008-0250-x 10.1002/(SICI)1096-9853 10.1016/j.cma.2013.08.010 10.1016/S0045-7825(96)01134-6 10.1007/s00466-021-02119-w 10.1061/(ASCE)GM.1943-5622.0001079 10.1016/j.ijsolstr.2017.04.030 10.1016/j.cma.2018.10.030 10.1002/nme.1620210210 10.1016/j.compgeo.2021.104061 10.1007/978-1-4020-6577-4_6 10.1017/CBO9780511755446 10.1145/174462.156635 10.1007/978-3-540-75103-8_1 10.3390/app112411893 10.1007/s00466-013-0835-x 10.1002/nag.3016 10.1007/s00466-020-01867-5 10.1016/j.cma.2017.07.028
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SubjectTerms	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
Title	Comparison of elements and state-variable transfer methods for quasi-incompressible material behaviour in the particle finite element method
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