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



I. Introduction



IV. Results

V. Conclusions

OUTLOOK

CEMUC



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.



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



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.)



CEMUC

I. Introduction



IV. Results

V. Conclusions

OUTLOOK



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



CEMUC

Remapping basis

Donor mesh Target mesh (State variable ) (Unload)

Transfer Operator


Incremental Volumetric Remapping



CEMUC

Step 1 – Divide all donor elements in 8 Gauss Volumes

Gauss Volume

Gauss Point



2D case view: Quadrilateral meshes overlay

Homogeneous

properties

Step 1



(Step 1)

CEMUC

Step 2 – For each target element to treat: division in 8 Gauss Volumes to remap




Step 2



CEMUC

Step 3 – Intersect each target Gauss volume with the donor Gauss volumes




Step 3 (Step 2)



CEMUC

Step 4 – For each target Gauss volume: Gauss volume division



2D case view: Quadrilateral meshes

Step 4

NL

Gauss

volume part

(Step 3)



CEMUC

Step 5 – For each target Gauss Volume part centroid:

Find the donor Gauss volume that encloses it



3

1

1

NLi

jNGj

iii tot

V

V

Remap state variable calculus

Weighted average as function of

the intersection Gauss volumes



CEMUC

I. Introduction



IV. Results

V. Conclusions

OUTLOOK



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)



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



CEMUC

Remapping operation: Comparison of methods

Remapping operation tests

NUMERICAL EXAMPLE

Standard extrapolation-interpolation method


State variable analysed: sxx stress

Original

Mesh

Remeshed

Mesh

Remap

Remap 2

Test methodology

Stage 2

1



CEMUC

I. Introduction



IV. Results

V. Conclusions

OUTLOOK



CEMUC

Remapping operation: Error comparison of the methods (IVR - NL5)


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%



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)


Results


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%



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)


Results


X = 54.7 X = 12.4

– 77%



CEMUC

I. Introduction



IV. Results

V. Conclusions

OUTLOOK



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

IVR Incremental Volumetric Remapping Method NUMISHEET 2005

Technology

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