ICME SummaryMark Horstemeyer

CAVS Chair Professor in Computational Solid Mechanics

Mechanical EngineeringMississippi State University

mfhorst@me.msstate.edu

1. ICME can reduce the product development time by alleviating costly trial-and error physical design iterations (design cycles) and facilitate far more cost-effective virtual design optimization.

2. ICME can reduce product costs through innovations in material, product, and process designs.

3. ICME can reduce the number of costly large systems scale experiments.

4. ICME can increase product quality and performance by providing more accurate predictions of response to design loads.

5. ICME can help develop new materials.6. ICME can help medical practice in making

diagnostic and prognostic evaluations related to the human body.

Six Advantages of Employing ICME in Design

1. Downscaling and upscaling: Only use the minimum required degree(s) of freedom necessary for the type of problem considered

2. Downscaling and upscaling: energy consistency between the scales

3. Downscaling and upscaling: verify the numerical model’s implementation before starting calculations

4. Downscaling: start with downscaling before upscaling to help make clear the final goal, requirements, and constraints at the highest length scale.

Eight Guidelines for Multiscale Bridging

5. Downscaling: find the pertinent variable and associated equation(s) to be the repository of the structure-property relationship from subscale information.

6. Upscaling: find the pertinent “effect” for the next higher scale by applying ANOVA methods

7. Upscaling: validate the “effect” by an experiment before using it in the next higher length scale.

8. Upscaling: Quantify the uncertainty (error) bands (upper and lower values) of the particular “effect” before using it in the next higher length scale and then use those limits to help determine the “effects” at the next higher level scale.

Eight Guidelines for Multiscale Bridging

Process-Structure-Property Modeling and the Associated

History

Requires: 1. theory, 2. computations, and 3. experiments

1. Requirements

Integrated Computational Materials Engineering (ICME)

1. Requirements

Integrated Computational Materials Engineering (ICME)

2.

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1. Requirements

Integrated Computational Materials Engineering (ICME)

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1. Requirements

4. Process-Structure-Property Modeling

Integrated Computational Materials Engineering (ICME)

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Length Scale Constitutive Model

Computational Code

Vernacular

StructuresMacoscale

Internal State Variable (ISV)

ABAQUS, Dyna Continuum Theory

PhasesMesoscale

Phase Field CALPHAD Mesomechanics

AtomsNanoscale

Modified Embedded Atom

Method

LAMMPS, Dynamo Molecular Dynamics/Statics.

Atomistics

ElectronsElectronic Scale

Density Funcitonal Theory

VASP First Principles, Ab-Initio,

Electronics

Density Functional Theory (DFT)

Modified Embedded Atom Method (MEAM)

Phase Field

Internal State Variable Theory (ISV)

Coh

esiv

e E

ner

gy, E

last

ic M

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Ph

ase

Coe

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s

Ela

stic

mod

uli

, ele

ctro

mag

neti

c pr

oper

ties

Ph

ase

Str

esse

s

Ph

ase

Com

p.

Multiscale Modeling Disciplines

Solid Mechanics: HierarchicalNumerical Methods: ConcurrentMaterials Science: HierarchicalPhysics: HierarchicalMathematics: Hierarchical and

Concurrent

continuum

electrons

atoms

dislocations

grains

Concurrentretain

only the minimal amount

of informati

onHierarchical

Macroscale ISV Continuum

Bridge 1 = Interfacial Energy, Elasticity

Atomistics(EAM,MEAM,MD,MS,

NmBridge 2 = Mobility

Bridge 3 = Hardening Rules

Bridge 4 = Particle Interactions

Bridge 5 = Particle-Void Interactions

Bridge 12 = FEA

ISV

Bridge 13 = FEA

DislocationDynamics (Micro-3D)

100’s Nm

ElectronicsPrinciples (DFT)

Å

Crystal Plasticity(ISV + FEA)10-100 µm

Crystal Plasticity(ISV + FEA)µm

CrystalPlasticity

(ISV + FEA)100-500µm

Bridge 6 =Elastic Moduli

Bridge 7 =High Rate

Mechanisms

Bridge 8 =Dislocation

Motion

Bridge 9 =Void \ Crack

Nucleation

Bridge 10 =Void \ Crack

Growth

Macroscale ISV ContinuumBridge 11 =void-crack

interactions

Multiscale Experiments

IVS ModelVoid Growth

Void/Void CoalescenceVoid/Particle Coalescence

Fem AnalysisIdealized Geometry

Realistic RVE GeometryMonotonic/Cyclic Loads

Crystal Plasticity

ExperimentFracture of SiliconGrowth of Holes

ExperimentUniaxial/torsion

Notch TensileFatigue Crack Growth

Cyclic Plasticity

FEM AnalysisTorsion/Comp

TensionMonotonic/Cyclic

Continuum ModelCyclic Plasticity

Damage

Structural Scale

Experiments FEM

ModelCohesive Energy

Critical Stress

AnalysisFracture

Interface Debonding

Nanoscale

ExperimentSEM

Optical methods

ISV ModelVoid Nucleation

FEM AnalysisIdealized GeometryRealistic Geometry

Microscale

Mesoscale

Macroscale

ISV ModelVoid Growth

Void/Crack Nucleation

ExperimentTEM

1. Exploratory exps2. Model correlation exps3. Model validation exps

OptimalProductProcess

Environment(loads, boundary

conditions)

Product(material, shape,

topology)

Process(method,

settings, tooling)

Design Options

Cost Analysis

Modeling

FEM Analysis

Experiment

Multiscales

Analysis Product &

Process Performance

(strength, reliability,

weight, cost, manufactur-

ability )

Design Objective & Constraints

Preference & Risk Attitude

Optimization under Uncertainty

Design Optimization

CyberInfrastructure

Engineering tools (CAD, CAE, etc.)

Conceptual design process(user-friendly interfaces)

IT technologies(hidden from the engineer)

Issues: Various sources of uncertainty across length and time scales:How should the bridge be designed?

Key research issue for metals and polymers (nanocomposites, humans, and animals)

Multiscale

Material Models

Length

Material/Structure Response

Remote SensorSystem

Safety/Human System

Response

Human Response

In-situ Accident

Bio

-In

spir

edP

rote

ctio

n S

yste

m (

BIP

S)

ISVs

Design performance

Robustness & Reliability

Uncertain loads & boundary conditions

Time

ProductPerformanceMaterial Processing Accident

ISVs

Pre-AccidentDesign

Validated Multiscale Models in a Cyberdesign Framework for Safety

Produc

MetalsStructuresContinuum elementGrainParticles/DefectsPPTsDislocationsAtomsElectrons

Production Level ModelingSynthetic PolymersStructuresContinuum elementFibersHard PhasesEntanglementsCrosslinksChainsMoleculesAtomsElectrons

Biological PolymersHuman bodyTendonFasciclesFibrilsMicroFibrilsCollagenMoleculesAtomsElectrons

Research Level Modeling

Research to Development to Application Philosophy

Hierarchical Structure Leads to Hierarchical Multiscale Modeling

I II III

Regime I: Elastic mechanisms such as bond stretching and chain rotation

Regime II: Strain softening induced by slippage of blocks of polymeric chains (polymeric chains having enough energy too overcome their energy barrier)

Regime III: Chain alignment and chain stretching/rotation between entanglements

Chains slippage

Chain alignment in the loading direction (Anisotropy)

Defects: entanglement points

Bouvard et al., Acta Mechanica, accepted

ISV model development: Mechanical characterization of amorphous polymer

Bond stretching

Bond torsionVan der Waals

Nanoscopic specimen of idealizedLinear amorphous polyethylene under

uniaxial tension (T=100K, nc=200, n_monomers=1000)

Typical terms inInter-atomic potential

Bond angle

Van der Waals interaction

Chains alignment (bond torsion)

Studying Polymers with Molecular Dynamics

) T, ,ε ε, ( fσ ,

σ

εObservable State Variables(strain, strain rate, temperature) Internal State Variables

(dislocations, damage)

length scale 1: nanoscale

length scale 2: submicron scale

length scale 3: microscale

length scale 4: macroscale

stress

strain

Schematic showing the stress-strain responses at four different size scales.

10-6

10-5

0.0001

0.001

0.01

0.1

1

10-10 10-8 10-6 0.0001 0.01 1

yiel

d s

tres

s/el

asti

c m

odu

lus

size (m)

large scale experiments

EAM calculations

indentation and torsion

experiments

interfacial forcemicroscopy experiments

Horstemeyer, M.F., Baskes, M.I., and Plimpton, S.J., “Computational Nanoscale Plasticity Simulations Using Embedded Atom Potentials,” Prospects in Mesomechanics, ed. George Sih, Theoretical and Applied Fracture Mechanics, Vol. 37, No. 1-3, pp. 49-98, 2001.

Macroscale ISV Continuum

Bridge 1 = Energy, Elasticity

Atomistics(EAM,MEAM,MD,M

S,

NmBridge 2 = Dislocation Mobilities

Bridge 3 = Hardening Rules

Bridge 12 = FEA

DislocationDynamics (Micro-3D)

100’s Nm

Electronics

Principles (DFT)

Å

Crystal Plasticity(ISV + FEA)

µm

Bridge 9 =

polycrystal stress-

strain behavior

Macroscale ISV Continuum

Bridge 6 =

Elastic Moduli

Bridge 7 =High Rate Mechanis

ms

Bridge 8 =dislocation density and yield

Can I create a formedcomponentwithout anexperiment?with multiscalemodeling?

QuantifyPerformanceParametersFirst!!!