1. Multiscale Modeling: An Overview
Dr. Mark Horstemeyer CAVS Chair Professor ASME Fellow Mississippi State University

2. Outline Modeling Philosophy Overview
MSU Internal State Variable Plasticity-Damage Model (MSU DMG 1.0) Theory
Horstemeyer, M.F., Lathrop, J., Gokhale, A.M., and Dighe, M., “Modeling Stress State Dependent Damage Evolution in a Cast Al-Si-Mg Aluminum Alloy,” Theoretical and Applied Fracture Mechanics, Vol. 33, pp , 2000
Bammann, D. J., Chiesa, M. L., Horstemeyer, M. F., Weingarten, L. I., "Failure in Ductile Materials Using Finite Element Methods," Structural Crashworthiness and Failure, eds. T. Wierzbicki and N. Jones, Elsevier Applied Science, The Universities Press (Belfast) Ltd, 1993.
Image Analysis Tool 1.0 User’s Tutorial
DMGfit 1.0 User’s Tutorial
MSU MultiStage Fatigue Model (MSU MSF 1.0) Theory
McDowell, D.L., Gall, K., Horstemeyer, M.F., and Fan, J., “Microstructure-Based Fatigue Modeling of Cast A356-T6 Alloy,” Engineering Fracture Mechanics, Vol. 70, pp.49-80, 2003.
MSFfit 1.0 User’s Tutorial
MSU ISV Thermoplastic Model (MSU TP 1.0) Theory
J.L. Bouvard, D.K. Ward, D. Hossain, E.B. Marin, D.J. Bammann, and M.F. Horstemeyer, “A General Inelastic Internal State Variable Model for Amorphous Glassy Polymers,” submitted to Acta Mechanica
TPfit 1.0 User’s Tutorial

3. Computational Manufacturing
and Design
Mission: We couple multidisciplinary research of solid mechanics, materials, physics, and
applied mathematics in three synergistic areas: theoretical modeling, experimentation, and
large scale parallel computational simulation to optimize design and manufacturing processes.

4. Multiscale Modeling ISV Bridge 12 = FEA ISV ISV Bridge 11 = FEA
Macroscale ISV Continuum
Macroscale ISV Continuum
Void \ Crack Interactions
Bridge 10 = Void \ Crack Growth µm
Crystal Plasticity (ISV + FEA)
Crystal Plasticity (ISV + FEA) µm
Bridge 5 = Particle-Void Interactions
Bridge 9 = Void \ Crack Nucleation µm
Bridge 8 = Dislocation Motion
Bridge 4 = Particle Interactions
Crystal Plasticity (ISV + FEA)
Bridge 7 = High Rate Mechanisms
Bridge 3 = Hardening Rules
100’s Nm
Dislocation Dynamics (Micro-3D)
Bridge 6 = Elastic Moduli
Bridge 2 = Mobility Nm
Atomistics (EAM,MEAM,MD,MS,
Bridge 1 = Interfacial Energy, Elasticity Å
Electronics Principles (DFT)

5. Multiscale Experiments
1. Exploratory exps
2. Model correlation exps
3. Model validation exps
Structural Scale
Experiments
FEM
Nanoscale
Macroscale
Continuum Model
Cyclic Plasticity
Damage
Experiment
Uniaxial/torsion
Notch Tensile
Fatigue Crack Growth
Cyclic Plasticity
Model
Cohesive Energy
Critical Stress
Analysis
Fracture
Interface Debonding
FEM Analysis
Torsion/Comp
Tension
Monotonic/Cyclic
Experiment
TEM
Microscale
ISV Model
Void Nucleation
Mesoscale
IVS Model
Void Growth
Void/Void Coalescence
Void/Particle Coalescence
Experiment
SEM
Optical methods
ISV Model
Void Growth
Void/Crack Nucleation
Experiment
Fracture of Silicon
Growth of Holes
FEM Analysis
Idealized Geometry
Realistic Geometry
Fem Analysis
Idealized Geometry
Realistic RVE Geometry
Monotonic/Cyclic Loads
Crystal Plasticity

6. Design Optimization Optimization under Uncertainty Analysis
Cost Analysis
Model
FEM Analysis
Experiment
Multiscales
Analysis
Product
(material, shape, topology)
Process (method, settings, tooling)
Design Options
Product & Process Performance
(strength, reliability,
weight, cost, manufactur-ability )
Design Objective & Constraints
Preference & Risk Attitude
Optimal
Product
Process
Environment
(loads, boundary conditions)
ISV

7. CyberInfrastructure IT technologies (hidden from the engineer)
Conceptual design process
(user-friendly interfaces)
Engineering tools
(CAD, CAE, etc.)
Strategic Goal #4 Cyberinfrastructure and information systems integration (related to Thrust 4)
Create and demonstrate integrated system of information tools for rapid concurrent design of
engineered components, assemblies, and the associated manufacturing processes incorporating
associated technologies.
Objectives
1. Create and demonstrate the framework for integrating design toolkits and
computational analysis tools with multiscale materials models, including interfaces to industry standard
commercial tools.
2. Create and demonstrate common easy-to-use design environment configurable for multilevel users
with distributed, concurrent, collaborative access.
3. Create means to transparently utilize computational grid resources with distributed computational
and information resources.
4. Create and demonstrate extensible, adaptive design framework with decision support, knowledge
accumulation, and support for incorporating business cost models.
5. Create and demonstrate tools and utilities for rapidly creating rule-based applications.
The cyber-infrastructure addresses concerns/issues at various levels/layers.
At the top, are engineers and the problems they are solving (shown in the center panel above). At this layer, we are addressing issues related to user interfaces and knowledge capture & semantics.
At the second layer (from the top) we are addressing issues related to individual applications and programming of parallel codes (shown in the right panel). These applications need to be engineered so as to allow integration with other application. Knowledge representation is an issue to be addressed here.
At the third layer, we are addressing application integration and interfaces (also shown in the right panel).
At the bottom layer, we are addressing issues related to IT enabling technologies (e.g., Grids, portals, web, security) and organizational issues such as service level agreements.

8. ARM LIGHTWEIGHT DESIGN
GM CADILLAC CONTROL
ARM LIGHTWEIGHT DESIGN
(2000) D C B A E
Standard FEA
Stress
(from highest
to lowest)
Inclusion
(from most severe
to less severe)
Damage
Objective: To employ multiscale material modeling
to reduce the weight of components
Truth!
Wrong!
initial failure site
(a)
(b)
Region 3
Region 1
model
experiment
Result: To optimize a redesign such that
25% weight saved
50% increase in load-bearing capacity
100% increase in fatigue life
$2 less per part

9. Internal State Variable
GM Corvette Cradle
Magnesium Design (2005)
System
Subsystem
Component
Internal State Variable
Plasticity-Damage
Simulation
Structures
Pore size
Nearest Neighbor Distance
Dendrite Cell Size
Porosity
Boundary Conditions
Panic brake
Pothole strike
Forces
Moments

10. Cradle Load-to-Failure
Simulation Results E D B A C F
Modern FEA answer
True answer
Modern Materials Science answer

11. Powder Metal FC0205 Steel (2008)
Compaction, Sintering, and Performance
model
experiment
failure predicted by damage model under performance with distribution of initial porosity
maximum von Mises Stress
Note: standard FEA would
have given the wrong location

12. Immersion and Image Analysis Densities by Zone
I – Compaction Modeling (Validation)
Main Bearing Cap – Green Density Distribution- after Springback (g/cc)
FEA Model
Geometry and Material Solution imported from ABAQUS/ Explicit to ABAQUS/Standard for Elastic Springback Analysis
Experiment
X-ray CT
Volume grows 0.6%
after springback
density
2D X-Ray CT
FEA 205Q
Experiment
Immersion and Image Analysis Densities by Zone
Density (g/cc)
+7.00
+6.90
+6.85
+6.80
+6.75
+6.70
+6.65
+6.60
+6.55
+6.95
+6.50
+6.45
+6.40
+7.05 1 3 2 4 5 7 8 10 11 6 12 13 16 15 17 18 14 19 20 9
Density Immersion 9 1 3 2 4 5 7 8 10 11 6 12 13 16 15 17 18 14 19 20
Image Analysis

13. Cyberinfrastructure Design Framework
FEA
simulation
Experimental
data
FEA
outputs
MSF
Validation
Input
deck
Design
objectives/
requirements
Boundary
conditions/
loading
FEA
setup
Optimization
Geometry
Mesh
CAD
Post-
processing
directives
Material
Material
properties
repository
Material
models and
constants
Model
calibration
Compute
platform
settings

14. MSU Multiscale Modeling
Vision: In 5-10 years, we are internationally recognized as the premiere material modeling group in world for our validated and verified research and production models
Mission: systemize our multiscale modeling capability so that the cyberinfrastructure easily admits each different aspect of the modeling characteristics (codes, materials info, mechanical properties tests, multiscale models, etc)

15. Modeling History and Overview
Started in thermonuclear weapons design at Sandia (no underground systems level testing)
Populate the space of systems levels with simulations (simulation based design and multiscale modeling to get correct physics)
Used for many different metal alloys in materials processing and life-performance analysis
Tech transfer to Navy, Army, and automotive applications
Notion of history modeling with internal state variables

16. FEA Simulations and Timeline Using Internal State Variable Model
Early 1980’s: steel alloys for weapon laydown event (highlight: front cover of Science) plasticity, damage, and fracture
Mid 1980’s-1990’s: forging process: rex
Late 1980’s: analysis of various components: plasticity and failure
Early 1990’s: Navy submarines lethality, welding
Mid 1990’s: forming, extrusion, heat treatment
Late 1990’s: automotive castings
Early 2000’s: everything automotive
Mid 2000’s: Army vehicle component designs
Late 2000’s: polymers and powder metals

17. Metals Modeled by Macroscale DMG ISV Plasticity-Damage Model 1.0
Steel Alloys (15)
A286, AF, C1008, S7tool, 1020, 10b22, 4140, 4340, 210SS, 304LSS, 319SS, HY80, HY100, HY130, FC0205
Aluminum Alloys(16)
1100, 2024T0, 2024T35, 2024T4, 5083, 5086, 6061T0, 6022, 6050, 6061T0, 6061T6, 7039, 7075T0, 7075T6, A319, A356
Magnesium Alloys (7)
AM20, AM30, AM50, AM60, AZ31, AZ91, AE44
Titanium Alloys (4)
Ti7Al4Mo, Ti8Al1Mo1V, Ti0Al6V4, Ti6Al6V2Sn
Uranium Alloys (2)
D38, D380075Ti
Nickel (2)
99.99% pure, In718
Brass (1)
99% pure
70 metal alloys to date!

18. MSU CAVS CMD Material Modeling Philosophy
Classical Modeling Paradigm
MSU CAVS Modeling Paradigm
Phenomena N=Model N
Phenomena N=Model 1 . .
Phenomena 3=Model 3
Phenomena 3=Model 1+few additional constants
Phenomena 2=Model 2
Phenomena 2=Model 1+few additional constants
Phenomena 1=Model 1
Phenomena 1=Model 1
Note: with each new model, many more
constants are introduced with the new
model
Note: with every new phenomena the model
moves back to a general abstraction so if the new
constants are zero the original model results

19. Example of Philosophies with Creep and Plasticity
Classical Modeling Paradigm
MSU CAVS Modeling Paradigm
Phenomena N=Model N
Phenomena N=Model 1 . .
Damage=Johnson-Cook
Damage=Garafalo+disl ISVs+Damage ISVs
Plasticity=Ramberg-Osgood
Plasticity=Garafalo + dislocation density ISVs
Creep=Nabarro-Herring Model
Creep=Garafalo flow rule
Note: with each new model, many more
constants are introduced with the added
new model
Note: with every new phenomena the model
moves back to a general abstraction so if the new
constants are zero the original model results

20. Macroscale Research and Production Models
Note 1: Production models/codes must have a documented citable journal article for
each version of the code
a. makes impact factor greater
b. makes it easier for next graduate student to add incremental improvements
Note 2: Production models/codes must build on the previous work
a. helps systemize and synergize our efforts in terms of research and funding
b. clears up confusion to outsider customers and industry
c. helps user base
Note 3: Production models/codes must have a theoretical and user’s manual
a. absolute necessity for new graduate students and new user’s
b. helps the broad usage of the model over time
c. this alone may lead the greatest impact over time
Note 4: Only a Production model/code can go into the cyberinfrastructure

21. Journal Article History and MSU CAVS R&D Modeling Plan
Bammann (1990) temperature and strain rate dependent unified-creep plasticity model
(Bammann Model)
Bammann et al. (1993) applications of Bammann model with damage (no formal name)
BCJ (1995) formalization of model (really mod of 1993 paper: BCJ)
Horstemeyer et al. (2000) microstructure with damage (DMG model)
Research
Production
EMMI
MSU CAVS DMG ISV Model 1.0
Version 1.1
Elastic mod
damage
(Allison)
Recrystallization/grain growth
V&V ?
Coalescence
(Allison,
Oglesby)
Version 1.2
Add more materials with quantifying
the structure-property relations
Pressure
Dep yield
(Hammi)
Version 1.3
Anisotropic
Damage
(Solanki)
Version 1.4

22. MSU CAVS R&D Modeling Plan (cont)
Research
Production
MSU CAVS DMG ISV Model 1.0
Version 1.5
Hardening
change
(Bammann)
V&V
High rate
Stress state
Dep
(Tucker)
Version 1.6
Subscale
studies
Plastic spin
(Najafi)
Version 1.7
Twinning
(Oppedal,
Bammann,
Horstemeyer,
Marin)
Version 1.8
Version 2.0 (new set
of constants required
for all materials)
EMMI

23. MSU CAVS R&D Modeling Plan (cont)
Research
Production
MSU CAVS ND DMG ISV Model 2.0
Version 2.1
PPT
morphology
(El Kadiri)
V&V
Nonlocal
damage
(Solanki)
Version 2.2
Subscale
studies
Phase
Transform
(LWang)
Version 2.3
Solidification
(Felicelli,
LWang)
New name??

24. Validation and Verification (V&V)
Research FE Codes
Tahoe
Ramaswamy code (nonlocal damage, implicit)
Winters code (coupled thermomechanical)
ABAQUS
model
Fitting algorithm
(Carino)
Production FE Codes
ABAQUS
LS Dyna
ESI Pamcrash
ESI Pamstamp
MD Nastran
Model implementation
Model
verification

25. Metals Modeled by MultiStage Fatigue Model 1.0
Steel Alloys (3)
4140, 319SS, FC0205
Aluminum Alloys(5)
2024T0, 7075T6, A319, A356, A380
Magnesium Alloys (7)
AM30, AM50, AM60, AZ31, AZ61, AZ91, AE44
15 metal alloys to date!
Polymers Modeled by MultiStage Fatigue Model 1.0
Polyurethane (2)
Pure, carbon nanotube polyurethane
Elastomer (2)
SBR, track rubber
Polycarbonate (1)

26. Journal Article History and MSU CAVS R&D Modeling Plan
McDowell et al (2003) microstructure-sensitive MultiStage Fatigue (MSF)
Xue et al (2007) grain size and texture effects
Jordon et al (2008) nearest neighbor distance and elastic moduli effect on porosity
Research
Production
MSU CAVS MSF Model 1.0
Version 1.1
Polymers
(Bouvard,
Brown)
V&V
Add more materials with quantifying
the structure-property relations
Corrosion
(???)
Version 1.2
Symptotic
Expansions
ISVs (???)
Version 1.3
Thermo
mechanical
(???)
Version 1.4

27. Polymers Modeled by Macroscale ISV ViscoElastic-ViscoPlasticity-Damage Model 1.0
Polycarbonate (1)
Polypropylene (1)
Polyurethane (1)
ABS
Elastomer (3-Santoprene, natural rubber, SBR)
Nylon (4)
Nylon 6.6, Nylon 4.4, E-glass+Nylon, S-glass+Nylon
Kevlar
Brain
Liver
Tendon
Placenta
12 polymers to date!

28. Journal Article History and ISV Polymer Modeling Plan
Bammann (1990) temperature and strain rate dependent unified-creep plasticity model
Bammann et al. (1993) applications of Bammann model with damage
BCJ (1995) formalization of model
Horstemeyer et al. (2000) microstructure with damage
Research
Production
Boyce-Arruda
Anand
MSU CAVS Poly DMG ISV Model 1.0
Version 1.1
viscoelasticity
(Prabhu)
V&V ?
rubbers
(Brown)
Version 1.2
Add more materials with quantifying
the structure-property relations
nanocomposites
(Lacy, Shi, Zhang,
Pittman, Toghiani)
Version 1.3

29. Model calibration tools development
CMD Theoreticians
THaupt/CCG
Tool & Status
DMG
ImageAnalyzer
MSF
BB->VEP
EMMI
PQplot
MSC
Piecewise lines->DSR
DMG UMAT+Uncertainty
DMG VUMAT+Nucleation data
VPSC
MSF+amplitude loading
(Fung->Biomaterial?)
Dislocation ANN GUI
ImageStitcher
RPTpostprocessor
Web
service
Model
evaluation
routine
(Fortran,
MATLAB) F e d b a c k
RLCarino
Computational
backend
for model
(MATLAB)
Web-based
Users
PC-based
Stand-alone
executable
Production codes

30. Model code, Providers, Users
DMG
ImageAnalyzer
MSF
BB->VEP
EMMI
PQplot
MSC
Piecewise curves->DSR
DMG UMAT+Uncertainty
DMG VUMAT+Nucl. data
VPSC
MSF+amplitude loading
(Fung->Biomaterial?)
Dislocation ANN GUI
ImageStitcher
RPTpostprocessor
mfhorst
tnw7
mfhorst, bjordan
jeanluc
ebmarin
yhammi
(jeanluc)
kns3
aoppedal, haitham
Mfhorst,bjordan
(lwilliams)
ElKadiri
(bjordon)
(axue)
(various), S.Agnew, Y.Guo
(various)
yhammi, bjordon, paul, adrian
jeanluc, jef83
jcrapps
(USAMP-PM?)
sponder
kns3
aoppedal
(NGC?) ?
osama, (haitham’s student)
(axue’s student)
Production codes

31. Computational Manufacturing
and Design
Mission: We couple multidisciplinary research of solid mechanics, materials, physics, and
applied mathematics in three synergistic areas: theoretical modeling, experimentation, and
large scale parallel computational simulation to optimize design and manufacturing processes.