IVR Incremental Volumetric Remapping Method NUMISHEET 2005
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Transcript of IVR Incremental Volumetric Remapping Method NUMISHEET 2005
Application of the Incremental Volumetric
Remapping Method in the Simulation of
Multi-Step Deep Drawing Processes
A.J. Baptista*, J.L. Alves**, M.C. Oliveira*, D.M. Rodrigues*, L.F. Menezes*
* Department of Mechanical Engineering, University of Coimbra,
Polo II, 3030 Coimbra, PORTUGAL
** Department of Mechanical Engineering, University of Minho,
Campus de Azurém,4080-058,Guimarães, PORTUGAL
CENTRO DE ENGENHARIA MECÂNICA DA UNIVERSIDADE DE COIMBRA
THE 6th INTERNATIONAL CONFERENCE AND WORKSHOP ON NUMERICAL SIMULATION OF 3D SHEET FORMING PROCESSES
August 15-19, 2005, Detroit, Michigan, USA
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
CEMUC
OUTLOOK
I. Introduction
II. Remapping algorithms
III. Numerical example
IV. Results
V. Conclusions
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
I. Introduction
II. Remapping algorithms
III. Numerical example
IV. Results
V. Conclusions
OUTLOOK
CEMUC
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
INTRODUCTION
The Remapping operation CEMUC
Donor mesh Target mesh
Generic definition of a remapping procedure (2D example)
Remapping in the Nodes
Nodal Variables:
Force, displacement, etc.
Remapping in the Gauss Points
State Variables:
Stress, density, etc.
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
INTRODUCTION
Remapping characterization CEMUC
APPLICATION FIELDS
• Solid Mechanics
• Fluid Dynamics
• Combustion
• Multidisciplinary subjects
• Adaptive mesh operations
• Multigrid methods
• Texture mapping
• Trimming operations
REMAPPING
NECESSITY
• Keep the equilibrium state
• Minimize the transfer error
• Overall accuracy of the simulations
OPERATION REQUIREMENTS
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
INTRODUCTION
Remapping methodologies and features CEMUC
Remapping methodologies (X. Jiao and M.T. Heath 2004)
Pointwise interpolation and extrapolation
Area / Volume averaging (Rezoning techniques)
Mortar elements (Project the data interface of subdomains)
Common refinement (Intersection of two overlay meshes)
Specialized methods
Methods desirable features (M. M. Rashid 2002)
Self-consistency (Identity operator for the degenerate case)
Locality (Avoid wrong domain/interfaces contributions)
Freedom from excessive smoothing
Freedom from spurious local extremes
Potential to incorporate constrains (Equilibrium, yield criteria, etc.)
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
CEMUC
I. Introduction
II. Remapping algorithms
III. Numerical example
IV. Results
V. Conclusions
OUTLOOK
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
REMAPPING ALGORITHMS
CEMUC Standard method
Standard extrapolation-interpolation remapping
Donor mesh Target mesh
Original meshes Extrapolation Interpolation I Interpolation II
INCREMENTAL VOLUMETRIC REMAPPING – IVR
Using the finite element shape functions:
i i
i
Volume averaging method
Incremental / discrete intersecting volumes calculation
DD3TRIM
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
CEMUC
Remapping basis
Donor mesh Target mesh (State variable ) (Unload)
Transfer Operator
REMAPPING ALGORITHMS
Incremental Volumetric Remapping
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
CEMUC
Step 1 – Divide all donor elements in 8 Gauss Volumes
Gauss Volume
Gauss Point
REMAPPING ALGORITHMS
Incremental Volumetric Remapping
2D case view: Quadrilateral meshes overlay
Homogeneous
properties
Step 1
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
(Step 1)
CEMUC
Step 2 – For each target element to treat: division in 8 Gauss Volumes to remap
REMAPPING ALGORITHMS
Incremental Volumetric Remapping
2D case view: Quadrilateral meshes overlay
Step 2
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
CEMUC
Step 3 – Intersect each target Gauss volume with the donor Gauss volumes
REMAPPING ALGORITHMS
Incremental Volumetric Remapping
2D case view: Quadrilateral meshes overlay
Step 3 (Step 2)
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
CEMUC
Step 4 – For each target Gauss volume: Gauss volume division
REMAPPING ALGORITHMS
Incremental Volumetric Remapping
2D case view: Quadrilateral meshes
Step 4
NL
Gauss
volume part
(Step 3)
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
CEMUC
Step 5 – For each target Gauss Volume part centroid:
Find the donor Gauss volume that encloses it
REMAPPING ALGORITHMS
Incremental Volumetric Remapping
3
1
1
NLi
jNGj
iii tot
V
V
Remap state variable calculus
Weighted average as function of
the intersection Gauss volumes
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
CEMUC
I. Introduction
II. Remapping algorithms
III. Numerical example
IV. Results
V. Conclusions
OUTLOOK
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
CEMUC
NUMISHEET Benchmark#3: Channel Draw/Cylindrical Cup 2-Stage Test (DP600)
NUMISHEET Benchmark#3
Stage 1: Channel Draw
NUMERICAL EXAMPLE
Cyclic bending and unbending
Three layers in thickness direction
More elements in the longitudinal direction
Good in thickness gradients prediction
Deep-Drawing simulations: DD3IMP (Static Implicit)
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
CEMUC
NUMISHEET Benchmark#3: Channel Draw/Cylindrical Cup 2-Stage Test (DP600)
NUMISHEET Benchmark#3
Stage 2: Cylindrical Cup
NUMERICAL EXAMPLE
Intermediate State: Trimming
Specimen A
Plane-strain conditions
Homogenize the number of elements
in the two principal directions
+ Remeshing
359 45
4 64
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
CEMUC
Remapping operation: Comparison of methods
Remapping operation tests
NUMERICAL EXAMPLE
Standard extrapolation-interpolation method
Incremental Volumetric Remapping
State variable analysed: sxx stress
Original
Mesh
Remeshed
Mesh
Remap
Remap 2
Test methodology
Stage 2
1
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
CEMUC
I. Introduction
II. Remapping algorithms
III. Numerical example
IV. Results
V. Conclusions
OUTLOOK
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
CEMUC
Remapping operation: Error comparison of the methods (IVR - NL5)
Remapping operation tests
Results
Initial state Extrapolation-Interpolation IVR ( NL = 5 )
0
500
1000
1500
2000
2500
3000
3500
4000
5 25 45 65 85 105 125 145 165
Error [MPa]
Nu
mb
er
of
no
des
0
500
1000
1500
2000
2500
3000
3500
4000
5 25 45 65 85 105 125 145 165
Error [MPa]
Nu
mb
er
of
no
desX = 54.7 X = 29.8
– 45%
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
0
500
1000
1500
2000
2500
3000
3500
4000
5 25 45 65 85 105 125 145 165
Error [MPa]
Nu
mb
er
of
no
des
CEMUC
Remapping operation: Error comparison of the methods (IVR – NL10)
Remapping operation tests
Results
Initial state Extrapolation-Interpolation IVR ( NL = 10 )
X = 17.5
0
500
1000
1500
2000
2500
3000
3500
4000
5 25 45 65 85 105 125 145 165
Error [MPa]
Nu
mb
er
of
no
des X = 54.7
– 68%
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
0
500
1000
1500
2000
2500
3000
3500
4000
5 25 45 65 85 105 125 145 165
Error [MPa]
Nu
mb
er
of
no
des
0
500
1000
1500
2000
2500
3000
3500
4000
5 25 45 65 85 105 125 145 165
Error [MPa]
Nu
mb
er
of
no
des
CEMUC
Remapping operation: Error comparison of the methods (IVR – NL15)
Remapping operation tests
Results
Initial state Extrapolation-Interpolation IVR ( NL = 15 )
X = 54.7 X = 12.4
– 77%
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
CEMUC
I. Introduction
II. Remapping algorithms
III. Numerical example
IV. Results
V. Conclusions
OUTLOOK
THE 6th INTERNATIONAL NUMISHEET CONFERENCE “Application of the Incremental Volumetric Remapping Method
in the Simulation of Multi-Step Deep Drawing Processes”
CEMUC
Remarks and main conclusions
The developed IVR method of DD3TRIM prove to be a very effective
and straightforward way to remap a given mesh.
The method is both self-consistent and makes use of constrains
such as yield criteria conservation.
The mean error, the smoothing effects and gradients distortion, can be greatly
reduced when compared with the extrapolation- interpolation base methods.
The discrete approximation used for calculating the intersecting volumes is a
reliable option face the complex geometrical methods.
An adjustable parameter (NL) allows the accuracy control of the remapping
operation and also, the flexibility face the meshes dimensions and asymmetries.
Conclusions
Application of the Incremental Volumetric
Remapping Method in the Simulation of
Multi-Step Deep Drawing Processes
A.J. Baptista*, J.L. Alves**, M.C. Oliveira*, D.M. Rodrigues*, L.F. Menezes*
* Department of Mechanical Engineering, University of Coimbra,
Polo II, 3030 Coimbra, PORTUGAL
** Department of Mechanical Engineering, University of Minho,
Campus de Azurém,4080-058,Guimarães, PORTUGAL
CENTRO DE ENGENHARIA MECÂNICA DA UNIVERSIDADE DE COIMBRA
THE 6th INTERNATIONAL CONFERENCE AND WORKSHOP ON NUMERICAL SIMULATION OF 3D SHEET FORMING PROCESSES
August 15-19, 2005, Detroit, Michigan, USA