Adaptive smoothed FEM for forming simulations

Antonius H. van den Boogaard, J. Eberhardsteiner (Editor), W. Quak, H.J. Böhm (Editor), F.G. Rammerstorfer (Editor)

Research output: Contribution to conferenceAbstractOther research output

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Abstract

FEMsimulation of large deformations as occur in metal forming processes is usually accompanied with highly distorted meshes. This leads first to a reduction of accuracy and later to loss of convergence when implicit solvers are used. Remeshing can be used to reduce element distortion, but repeated remeshing will result in smoothing of data like equivalent plastic strain, due to averaging and interpolation. A meshless method circumvents the problem of mesh distortion, but depending on the integration of the weak formulation of equilibrium mapping of data and hence smoothing of data still remains unless a nodal integration scheme is used. Starting with a LocalMaximum Entropy approach [1] with nodal integration, we end-up with a smoothed Finite Element formulation in the limit of local approximations [2]. It is straightforward to adapt the triangulation in every increment, yielding an Adaptive Smoothed Finite Element Method, in which large deformations can be modelled with a Lagrangian description without the necessity to map data from one step to the other. A cell based stabilized conforming nodal integration method (SCNI) [3] is used. Depending on the configuration of nodes, nodal integration can yield singular stiffness matrices, resulting in spurious displacement modes [4]. A stabilization is used, based on minimizing the difference between a ‘linear assumed’ and the consistent strain field. The cells are based on the Delaunay triangulation, connecting mid-sides and centres of gravity of the triangles (Figure 1). Especially at the outer boundary, this yields a simpler formulation than using the dual Voronoi tesselation
Original languageEnglish
PagesCD-ROM-
Publication statusPublished - 10 Sep 2012
Event6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012 - Vienna, Austria
Duration: 10 Sep 201214 Sep 2012
Conference number: 6

Conference

Conference6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012
Abbreviated titleECCOMAS
CountryAustria
CityVienna
Period10/09/1214/09/12

Fingerprint

Finite element method
Triangulation
Metal forming
Stiffness matrix
Plastic deformation
Interpolation
Gravitation
Entropy
Stabilization

Keywords

  • METIS-288089
  • IR-81452
  • Onderzoek van algemene industriele aardMechanical engineering and technology

Cite this

van den Boogaard, A. H., Eberhardsteiner, J. (Ed.), Quak, W., Böhm, H. J. (Ed.), & Rammerstorfer, F. G. (Ed.) (2012). Adaptive smoothed FEM for forming simulations. CD-ROM-. Abstract from 6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012, Vienna, Austria.
van den Boogaard, Antonius H. ; Eberhardsteiner, J. (Editor) ; Quak, W. ; Böhm, H.J. (Editor) ; Rammerstorfer, F.G. (Editor). / Adaptive smoothed FEM for forming simulations. Abstract from 6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012, Vienna, Austria.
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van den Boogaard, AH, Eberhardsteiner, J (ed.), Quak, W, Böhm, HJ (ed.) & Rammerstorfer, FG (ed.) 2012, 'Adaptive smoothed FEM for forming simulations' 6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012, Vienna, Austria, 10/09/12 - 14/09/12, pp. CD-ROM-.

Adaptive smoothed FEM for forming simulations. / van den Boogaard, Antonius H.; Eberhardsteiner, J. (Editor); Quak, W.; Böhm, H.J. (Editor); Rammerstorfer, F.G. (Editor).

2012. CD-ROM- Abstract from 6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012, Vienna, Austria.

Research output: Contribution to conferenceAbstractOther research output

TY - CONF

T1 - Adaptive smoothed FEM for forming simulations

AU - van den Boogaard, Antonius H.

AU - Quak, W.

A2 - Eberhardsteiner, J.

A2 - Böhm, H.J.

A2 - Rammerstorfer, F.G.

PY - 2012/9/10

Y1 - 2012/9/10

N2 - FEMsimulation of large deformations as occur in metal forming processes is usually accompanied with highly distorted meshes. This leads first to a reduction of accuracy and later to loss of convergence when implicit solvers are used. Remeshing can be used to reduce element distortion, but repeated remeshing will result in smoothing of data like equivalent plastic strain, due to averaging and interpolation. A meshless method circumvents the problem of mesh distortion, but depending on the integration of the weak formulation of equilibrium mapping of data and hence smoothing of data still remains unless a nodal integration scheme is used. Starting with a LocalMaximum Entropy approach [1] with nodal integration, we end-up with a smoothed Finite Element formulation in the limit of local approximations [2]. It is straightforward to adapt the triangulation in every increment, yielding an Adaptive Smoothed Finite Element Method, in which large deformations can be modelled with a Lagrangian description without the necessity to map data from one step to the other. A cell based stabilized conforming nodal integration method (SCNI) [3] is used. Depending on the configuration of nodes, nodal integration can yield singular stiffness matrices, resulting in spurious displacement modes [4]. A stabilization is used, based on minimizing the difference between a ‘linear assumed’ and the consistent strain field. The cells are based on the Delaunay triangulation, connecting mid-sides and centres of gravity of the triangles (Figure 1). Especially at the outer boundary, this yields a simpler formulation than using the dual Voronoi tesselation

AB - FEMsimulation of large deformations as occur in metal forming processes is usually accompanied with highly distorted meshes. This leads first to a reduction of accuracy and later to loss of convergence when implicit solvers are used. Remeshing can be used to reduce element distortion, but repeated remeshing will result in smoothing of data like equivalent plastic strain, due to averaging and interpolation. A meshless method circumvents the problem of mesh distortion, but depending on the integration of the weak formulation of equilibrium mapping of data and hence smoothing of data still remains unless a nodal integration scheme is used. Starting with a LocalMaximum Entropy approach [1] with nodal integration, we end-up with a smoothed Finite Element formulation in the limit of local approximations [2]. It is straightforward to adapt the triangulation in every increment, yielding an Adaptive Smoothed Finite Element Method, in which large deformations can be modelled with a Lagrangian description without the necessity to map data from one step to the other. A cell based stabilized conforming nodal integration method (SCNI) [3] is used. Depending on the configuration of nodes, nodal integration can yield singular stiffness matrices, resulting in spurious displacement modes [4]. A stabilization is used, based on minimizing the difference between a ‘linear assumed’ and the consistent strain field. The cells are based on the Delaunay triangulation, connecting mid-sides and centres of gravity of the triangles (Figure 1). Especially at the outer boundary, this yields a simpler formulation than using the dual Voronoi tesselation

KW - METIS-288089

KW - IR-81452

KW - Onderzoek van algemene industriele aardMechanical engineering and technology

M3 - Abstract

SP - CD-ROM-

ER -

van den Boogaard AH, Eberhardsteiner J, (ed.), Quak W, Böhm HJ, (ed.), Rammerstorfer FG, (ed.). Adaptive smoothed FEM for forming simulations. 2012. Abstract from 6th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2012, Vienna, Austria.