the japan association for nonlinear cae and its v&v

Mechanical Design & Analysis Corporation

ASME 2012 Verification and Validation Symposium, Las Vegas, NV 1

May 3, 2012

Takaya Kobayashi1, Hiroto Ido2, Junji Yoshida3,

Hideo Takizawa4, and Kenjiro Terada5

1Mechanical Design & Analysis Corporation, 2LMS Japan,

3University of Yamanashi, 4Mitsubishi Materials Corporation, and 5Tohoku University

JAPAN

The Japan Association for Nonlinear CAE

and its V&V Related Activities

ASME 2012 Verification and Validation Symposium

May 2-4, 2012, Las Vegas, NV

11-1 Standards Development Activities for

Verification and Validation: Part 1

V&V2012-6109



“JANCAE” is a nonprofit organization, which was started in 2001 by the founder Professor Noboru Kikuchi of

University of Michigan, offers several activities to Japanese domestic companies, universities and software

vendors to gain a deeper understanding of nonlinear CAE.

A major activity of JANCAE is the CAE training course which is held twice a year. Cumulating total over 3,500

engineers participated to this training course through 2001 to 2012.

The Japan Association for Nonlinear CAE: a New Framework for CAE Researchers and Engineers

Participants Classification by Industry.

The numbers of participants reflect the overall industrial structure

of Japan, with its major sectors: automotive, electrical equipment

and so on.



Lecture Titles of JANCAE Training Course

Discretization Method for CAE

Particle Method

Coupled CAE Multiscale CAE

Nonlinear Material Model

Mechanics and its Method

Nonlinear Mathematics, Mechanics and FEM

Finite Elements in CAE

Basic Theory for CAE Numerical Solution Basics

Continuum Mechanics Basics

2002

2003

2004

2005

2006

2007

2008

2009

2010 CAE and Design

Nonlinear CAE Management

Material Model Selection

Element Selection

V&V

Strength and Stiffness Noise and Vibration Mechanical Dynamics

Material and Manufacturing

Reliability and Optimization

Linear vs. Nonlinear

Thermal Problems

CAE Benchmark

Element Technology

Nonlinear CAE for Multiphysics

Physical Model for CAE

Physical Validation

Complexity

Years

of

Experience

Year

I. Mathematical Foundations

II. Nonlinear Mechanics

III. Mechanical Design Skills

IV. CAE Management

V. Multiphysics

VI. Brake through to the Next Generation

The program of the training courses is structured in a first and second half, 2 days for each half.

The first half is for basics. The second half focuses on the applications as shown bellow.

The curriculum is well-thought-out, so that the participants can learn a wide variety of what CAE

covers today.



Independently from this CAE training course, JANCAE has organized “The Working Group on Material

Modeling” since 2005. More than 30 engineers and researchers from different organization, including

software vendors, join this working group.

The working group focuses on providing a practical approach to inelastic material modeling, that is

assigning an appropriate material model from a material library offered by commercial FE codes, and

determining proper material properties from material testing.

The Working Group on Material Modeling of JANCAE

The working group was originally started to study hyperelasticity

and viscoelasticity. Then, its research activities have diversified

into high speed tensile test of resin materials; coding user

subroutines soon followed.

High Speed Tensile Test of

Resin Materials, 2008

max 20 m/sec (44 mph)

PP specimen with dot print for DIC



Commercial FE codes offer user subroutine capabilities to extend material models. Users can implement their

required constitutive laws following programming rules that each code provides. However in reality, it is

difficult for ordinary users who are not familiar with the mathematical framework of continuum mechanics.

The Working Group of JANCAE started its unique R&D activity in 2009, called “Unified Material Model Driver

Project”.

User Subroutines for Constitutive Law in FE Codes

Strain-displacement relationship

uS

tS

V

},{ yx tt

},{ yx uux

y g

i

j

j

iij

x

u

x

u

2

10

i

j

jig

x

Equilibrium equation

}]{[}{ uKf Stiffness equation

Constitutive law

Stress integration

Consistent tangent matrix

f u

D

n

n+1

D

Displacement Force

Weak form integration

UMAT user subroutines



The principal purpose of the “Unified Material Model Driver (UMMD)” is to develop a set of standardized

subroutines for common use among commercial FE codes.

The working group’s first attempt was focused on the metal plasticity. Nowadays, many different yield

functions, including anisotropic behavior, are proposed in the field of sheet metal forming.

However, most commercial FE codes provide only limited kinds of yield functions, such as the classical Hill’s

anisotropic function. The UMMD project was meant to give ordinary users more convenient alternatives.

In our framework, updated stress and consistent tangent modulus are commonly calculated through UMMDp

and separated from each code’s specified input rule (variable definitions & stored formats) by a universal socket head.

Unified Material Model Driver for plasticity (UMMDp)

usermat ucmat2 ucmat3

umat** utan**

LUSR**(C) umat hypela2

Main for test

Updated Stress: {n+1} Consistent Tangent: [D/∂D]

Current Stress: {n} Inc. of strain: {D}

Universal socket head

Test_ ummdp

UMMDp

Unified Material Model Driver

for Plasticity

FE Codes Abaqus ANSYS ADINA LS-Dyna MSC.Marc Radioss

Check yield locus and differentials

von Mises

Hill 1948

Gotoh bi-quad

Barlat Yld2000

Yield functions

Stress {}

Eq.stress and its differentials

Barlat Yld2004

Barlat Yld89

Cazacu 2006

Karafills-Boyce

ummdp_ chkyf

Hill 1990

BBC2005

BBC2008

Vegter 2006

Hardening rules

Curve library

Isotropic Swift

Ludwick

Voce

Linear

Kinematic

Combined Prager

Ziegler

Chaboche

Armstrong

Test code or commercial codes Development subroutine



The universal socket head, which provide plug-and-play compatibility for UMMDp was developed in

cooperation with the Japanese branch offices of FE code vendors. We appreciate the contributions* of their

administration in the V & V activities.

The coding of UMMDp was successfully verified by the NAFEMS’s fundamental 2D plasticity benchmark

problem for von Mises yield criterion.

Code Verification 1: Code-to-Code Comparison

Step 1 Step 2 Step 3 Step 4

Step 5 Step 6 Step 7 Step 8 -10

-8

-6

-4

-2

0

2

4

6

8

10

-10 -8 -6 -4 -2 0 2 4 6 8 10 11-33 /MPa

22-

33 /

MPa

Built-in

UMMDp

Yield locus

Step 1 & 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step8

Line : FE code’s Built-in von Mises Plot : UMMDp

NAFEMS, 2.4 Fundamental

2D Plasticity Benchmark

Code-to-Code verification for von Mises yield surface

*Courtesy of Suzuki (Abaqus), Yamanashi (ADINA), Inoue (ANSYS), LS-DYNA (Ida) and Nagai (Marc)



Following yield functions were implemented to UMMDp.

Hill(1948, 1990), Gotoh's bi-quadratic, Barlat (Yld89, Yld2000, Yld2004), Banabic (BBC2005, BBC2008),

Cazacu 2006, Karafills & Boyce, and Vegter

The code verification was performed by the comparison between the yield surface in the original literatures

and UMMDp results. This verification study represents a potential performance of commercial FE codes for

advanced inelastic analysis.

Code Verification 2: Comparison with Literatures

Code verification by comparison with literatures*

*Courtesy of Takizawa, Mitsubishi Materials Corporation (Yld2000), and Tsunori, IHI (Cazacu)

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

x

y

xy/kxy=0.0

xy/kxy=0.2

xy/kxy=0.4

xy/kxy=0.6

xy/kxy=0.8

Original UMMDp Original UMMDp

Barlat Yld2000 (for Al alloy) Cazacu (for Ti or Mg alloy)



To demonstrate the practical application of UMMDp, we simulated a hydraulic bulge test of aluminum alloy

in cooperation with Prof. Kuwabara, Tokyo University of Agriculture and Technology.

They have reported the experimental data of thickness change of the sheet as well as Abaqus UMAT

(Yld2000) result by their collaborator, Prof. Jeong Whan Yoon, Swinburne University of Technology.

A code-to-code comparison to solve the small difference, and a validation study with the experimental

investigation are undergoing.

Code Verification 3: Comparison with Experiments

Code verification by comparison with hydraulic bulge test of aluminum alloy*

*T. Kuwabara, et al., Material Modeling of 6000 Series Aluminum Alloy Sheets with Different Density Cube Textures and Effect on the Accuracy of Finite Element Simulation, Proc. NUMISHEET 2011, Seoul, Korea, 21-26 August, 2011, pp.800-806.

Strain in thickness direction

r [mm]

Abaqus UMAT (Yld2000)

Experiment

UMMDp (Yld2000)



Future Expansion of UMMD for Rubber Materials

Hyperelastic branch

isochoric part

Hyperelastic branch with damage

Viscoelastic branches volumetric part

NEQU ̂

1 2 3

0

1

2

3

4

公称応力

[M

Pa]

伸張比 [-]

-3 -2 -1 0 1 2 3-3

-2

-1

0

1

2

3

せん断応力

[M

Pa

]

せん断ひずみ [-]

Stretch [-]

Shear strain [-]

Nom

inal st

ress

[M

Pa]

Nom

inal st

ress

[M

Pa]

Tensile

Shear

Hyperelastic and viscoelastic responses with damage effects

Stress reduction due to damage

Hysteresis loop due to viscoelasticity

Rubber materials exhibit hyperelastic and viscoelastic responses with damage effects.

The viscoelastic response represents stress relaxation in the time domain (hysteresis loop) and the damage

effect represents stress reduction by cyclic loading.

Simple Biaxial

Biaxial tension.MPG

Simple tension.wmv



UMMDr

Unified Material Model Driver

for Rubber

Updated Stress: n+1 Consistent Tangent: Cn+1

Deformation Gradient: Fn+1

History Variable: Hn

Universal socket head:

FE Codes:

ucmat2 ucmat3

Viscoelastic branch: Evolution eq.

Simo

Holzapfel

Reese-Govindjee

Hyperelastic branch: isochoric part

Simo

Miehe

Ogden- Roxburgh

Main for test

Test_ ummdr

function I

Ogden

Arruda-Boyce

Mooney Rivlin

Neo-Hookean Damage evolution

Hyperelastic branch: volumetric part

umat usermat umat** utan**

hypela2

Abaqus ANSYS ADINA LS-Dyna MSC.Marc

function II

Unified Material Model Driver for rubber (UMMDr) The concept of UMMD is also available for rubber modeling. The working group started prototyping in 2011

using ADINA capabilities.



Frequency-dependent finite strain viscoelastic responses under sinusoidal loading

f = 0.005, 0.05 and 0.5 Hz

Hyperelastic damage response under cyclic loading

Stretch ratio: 1 2 1 3 1 4 1 5 1

-3 -2 -1 0 1 2 3

-3

-2

-1

0

1

2

3

Deformation Gradient F13

1st P

iola

-Kirchh

off s

tre

ss P

12

UCMAT3Built-in,0.005 Hz



0 100 200 300 400

-3

-2

-1

0

1

2

3

Time [s]

De

form

atio

n G

rad

ien

t F

13

1 2 3 4 50

1

2

Stretch N

om

ina

l str

ess P

11

built-in

ucmat3

Code Verification 1: Code-to-Code Comparison

The code verification is partially undergoing for viscoelasticity and damage effect. These characteristics are

treated separately under present conditions.



Note One of the points to develop UMMDr is that the different FE codes have different measure of stress and

strain in the finite strain formulation of hyperelasticity. UMMDr provides a transformation capability which

works as necessary.

Jaumann rate of Cauchy stress

1 1, n n

cs 1 1 , :n n dc cs s

Updated Lagrangian

Tangent Stress and

1 1, :n n S S EC C

Total Lagrangian Tangent Stress 2nd P-Kstress and G-L strain

1 1, n n S C

Constitutive law

1 1, n n

cs

Jaumann rate of Kirchhoff stress

1, n nF q

deformation gradient and state variable

Interface Universal socket head

UMMDr

1 1, n n csTruesdell stress Transformation

if necessary

TL

UL

ULJK

ULJ



Conclusions The environment around nonlinear CAE will change further in the future. We will be required to have

better skills in many different situations.

JANCAE will be a new framework to raise the whole level of domestic CAE users and their individual skills

– both increases when we work with conscious people.

And also we would like to contribute to advances in V & V activities with you.

the japan association for nonlinear cae and its v&v

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