Efficient implicit simulation of incremental sheet forming

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Abstract

In single point incremental forming (SPIF), the sheet is incrementally deformed by a small spherical tool following a lengthy tool path. The simulation by the finite element method of SPIF requires extremely long computing times that limit the application to simple academic cases. The main challenge is to perform thousands of load increments modelling the lengthy tool path with elements that are small enough to model the small contact area. Because of the localised deformation in the process, a strong nonlinearity is observed in the vicinity of the tool. The rest of the sheet experiences an elastic deformation that introduces only a weak nonlinearity because of the change of shape. The standard use of the implicit time integration scheme is inefficient because it applies an iterative update (Newton–Raphson) strategy for the entire system of equations. The iterative update is recommended for the strong nonlinearity that is active in a small domain but is not required for the large part with only weak nonlinearities. It is proposed in this paper to split the finite element mesh into two domains. The first domain models the plastically deforming zone that experiences the strong nonlinearity. It applies a full nonlinear update for the internal force vector and the stiffness matrix every iteration. The second domain models the large elastically deforming zone of the sheet. It applies a pseudolinear update strategy based on a linearization at the beginning of each increment.Within the increment, it reuses the stiffness matrix and linearly updates the internal force vector. The partly linearized update strategy is cheaper than the full nonlinear update strategy, resulting in a reduction of the overall computing. Furthermore, in this paper, adaptive refinement is combined with the two domain method. It results in accelerating the standard SPIF implicit simulation of 3200 shell elements by a factor of 3.6.
Original languageEnglish
Pages (from-to)597-612
JournalInternational journal for numerical methods in engineering
Volume90
Issue number5
DOIs
Publication statusPublished - 2012

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Update
Stiffness matrix
Nonlinearity
Simulation
Increment
Tool Path
Domain Model
Stiffness Matrix
Elastic deformation
Linearization
Internal
Adaptive Refinement
Newton-Raphson
Shell Element
Elastic Deformation
Computing
Finite element method
Time Integration
System of equations
Reuse

Keywords

  • IR-80046
  • METIS-285670
  • Onderzoek van algemene industriele aardMechanical engineering and technology

Cite this

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title = "Efficient implicit simulation of incremental sheet forming",
abstract = "In single point incremental forming (SPIF), the sheet is incrementally deformed by a small spherical tool following a lengthy tool path. The simulation by the finite element method of SPIF requires extremely long computing times that limit the application to simple academic cases. The main challenge is to perform thousands of load increments modelling the lengthy tool path with elements that are small enough to model the small contact area. Because of the localised deformation in the process, a strong nonlinearity is observed in the vicinity of the tool. The rest of the sheet experiences an elastic deformation that introduces only a weak nonlinearity because of the change of shape. The standard use of the implicit time integration scheme is inefficient because it applies an iterative update (Newton–Raphson) strategy for the entire system of equations. The iterative update is recommended for the strong nonlinearity that is active in a small domain but is not required for the large part with only weak nonlinearities. It is proposed in this paper to split the finite element mesh into two domains. The first domain models the plastically deforming zone that experiences the strong nonlinearity. It applies a full nonlinear update for the internal force vector and the stiffness matrix every iteration. The second domain models the large elastically deforming zone of the sheet. It applies a pseudolinear update strategy based on a linearization at the beginning of each increment.Within the increment, it reuses the stiffness matrix and linearly updates the internal force vector. The partly linearized update strategy is cheaper than the full nonlinear update strategy, resulting in a reduction of the overall computing. Furthermore, in this paper, adaptive refinement is combined with the two domain method. It results in accelerating the standard SPIF implicit simulation of 3200 shell elements by a factor of 3.6.",
keywords = "IR-80046, METIS-285670, Onderzoek van algemene industriele aardMechanical engineering and technology",
author = "A. Hadoush and {van den Boogaard}, {Antonius H.}",
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doi = "10.1002/nme.3334",
language = "English",
volume = "90",
pages = "597--612",
journal = "International journal for numerical methods in engineering",
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}

Efficient implicit simulation of incremental sheet forming. / Hadoush, A.; van den Boogaard, Antonius H.

In: International journal for numerical methods in engineering, Vol. 90, No. 5, 2012, p. 597-612.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Efficient implicit simulation of incremental sheet forming

AU - Hadoush, A.

AU - van den Boogaard, Antonius H.

PY - 2012

Y1 - 2012

N2 - In single point incremental forming (SPIF), the sheet is incrementally deformed by a small spherical tool following a lengthy tool path. The simulation by the finite element method of SPIF requires extremely long computing times that limit the application to simple academic cases. The main challenge is to perform thousands of load increments modelling the lengthy tool path with elements that are small enough to model the small contact area. Because of the localised deformation in the process, a strong nonlinearity is observed in the vicinity of the tool. The rest of the sheet experiences an elastic deformation that introduces only a weak nonlinearity because of the change of shape. The standard use of the implicit time integration scheme is inefficient because it applies an iterative update (Newton–Raphson) strategy for the entire system of equations. The iterative update is recommended for the strong nonlinearity that is active in a small domain but is not required for the large part with only weak nonlinearities. It is proposed in this paper to split the finite element mesh into two domains. The first domain models the plastically deforming zone that experiences the strong nonlinearity. It applies a full nonlinear update for the internal force vector and the stiffness matrix every iteration. The second domain models the large elastically deforming zone of the sheet. It applies a pseudolinear update strategy based on a linearization at the beginning of each increment.Within the increment, it reuses the stiffness matrix and linearly updates the internal force vector. The partly linearized update strategy is cheaper than the full nonlinear update strategy, resulting in a reduction of the overall computing. Furthermore, in this paper, adaptive refinement is combined with the two domain method. It results in accelerating the standard SPIF implicit simulation of 3200 shell elements by a factor of 3.6.

AB - In single point incremental forming (SPIF), the sheet is incrementally deformed by a small spherical tool following a lengthy tool path. The simulation by the finite element method of SPIF requires extremely long computing times that limit the application to simple academic cases. The main challenge is to perform thousands of load increments modelling the lengthy tool path with elements that are small enough to model the small contact area. Because of the localised deformation in the process, a strong nonlinearity is observed in the vicinity of the tool. The rest of the sheet experiences an elastic deformation that introduces only a weak nonlinearity because of the change of shape. The standard use of the implicit time integration scheme is inefficient because it applies an iterative update (Newton–Raphson) strategy for the entire system of equations. The iterative update is recommended for the strong nonlinearity that is active in a small domain but is not required for the large part with only weak nonlinearities. It is proposed in this paper to split the finite element mesh into two domains. The first domain models the plastically deforming zone that experiences the strong nonlinearity. It applies a full nonlinear update for the internal force vector and the stiffness matrix every iteration. The second domain models the large elastically deforming zone of the sheet. It applies a pseudolinear update strategy based on a linearization at the beginning of each increment.Within the increment, it reuses the stiffness matrix and linearly updates the internal force vector. The partly linearized update strategy is cheaper than the full nonlinear update strategy, resulting in a reduction of the overall computing. Furthermore, in this paper, adaptive refinement is combined with the two domain method. It results in accelerating the standard SPIF implicit simulation of 3200 shell elements by a factor of 3.6.

KW - IR-80046

KW - METIS-285670

KW - Onderzoek van algemene industriele aardMechanical engineering and technology

U2 - 10.1002/nme.3334

DO - 10.1002/nme.3334

M3 - Article

VL - 90

SP - 597

EP - 612

JO - International journal for numerical methods in engineering

JF - International journal for numerical methods in engineering

SN - 0029-5981

IS - 5

ER -