Adaptive Multiscale Adaptive Multiscale Modeling and Simulation Modeling and Simulation

for Munitions Simulations*for Munitions Simulations*Progress ReportProgress Report

PIs: Jacob Fish and Mark S. ShephardPIs: Jacob Fish and Mark S. ShephardPost-docs: Gal Davidi, Caglar OskayPost-docs: Gal Davidi, Caglar OskayStudents: Zheng Yuan, Rong FanStudents: Zheng Yuan, Rong Fan

*AFRL support leveraged by support from NSF, ONR and General Motors

Roadmap of DevelopmentsRoadmap of DevelopmentsAssessment of commercial code Assessment of commercial code capabilitiescapabilities Mesh sensitivity studies (Gal Davidi) Mesh sensitivity studies (Gal Davidi) Validation studies (Rong Fan)Validation studies (Rong Fan)

Fragmentation capabilities for metalsFragmentation capabilities for metals Homogenization based approach (Gal Davidi)Homogenization based approach (Gal Davidi) Integration of homogenization in ABAQUS Integration of homogenization in ABAQUS

(Zhen Yuan) (Zhen Yuan) PUM based (Zhen Yuan and Rong Fan) PUM based (Zhen Yuan and Rong Fan)

Roadmap of Developments (cont)Roadmap of Developments (cont)Fragmentation capabilities for compositesFragmentation capabilities for composites Reduced order methodology (Oskay) Reduced order methodology (Oskay) Validation studies (Oskay)Validation studies (Oskay) Integration in ABAQUSIntegration in ABAQUS Multiscale Enrichment based PUM Multiscale Enrichment based PUM

ApplicationsApplications

Fragmentation in MetalsFragmentation in MetalsExperimental setupExperimental setup

Impactor in Sabot

Target Assembly

DH36 Steel Plate

The experimental parameters considered:• Steel target plate: DH36 steel; 3/16 inch thick; 6 inch diameter; • Impact velocity: In the range between 920 ft/sec. • Backing material: Polyurea: 0.215 inch• Impactor: non-deformable

Experiment vs ABAQUS simulationExperiment vs ABAQUS simulation (without backing) (without backing)

Mises stress (without backing)

Equivalent plastic strain (without backing)

Experiment vs SimulationExperiment vs SimulationDH36DH36

Drawbacks of commercial softwareDrawbacks of commercial software

0.00E+00

5.00E+04

1.00E+05

1.50E+05

2.00E+05

2.50E+05

3.00E+05

0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0.0004 0.00045

Fine (160)

Coarse (80)

Very Coarse (40)

3D models (4-8 layers)

Shell 21 layers

1.1. Cost of 3D simulations (4 days for 21 layer-model, Cost of 3D simulations (4 days for 21 layer-model, r-adaptivity)r-adaptivity)

2.2. Mesh dependency of both 3D and shell modelsMesh dependency of both 3D and shell models

3D model (21 layers)

Remedy: Multiscale EnrichmentRemedy: Multiscale Enrichment

Global (structure) EnrichmentGlobal (structure) Enrichment Enrich the kinematics of the global mesh with Enrich the kinematics of the global mesh with

failure characteristic (delamination, shear failure characteristic (delamination, shear banding, fragmentation) characteristic banding, fragmentation) characteristic computed on the local patchcomputed on the local patch

For computational efficiencyFor computational efficiency

Local (material) EnrichmentLocal (material) Enrichment Embed discontinuities (strong or weak) into Embed discontinuities (strong or weak) into

material (micromechanical) modelmaterial (micromechanical) modelFor regularization of failure modelsFor regularization of failure models

BetterBetter

Global Enrichment (MEPU)Global Enrichment (MEPU)

iN db b

Cell problems on

ijc

Q

Failure deformation mode-shapes

delamination

fracture

Global deformation modes

( )CoarseScale Enrichment

i i iA Au N d N ab b a ac= +G555555HG55H

xRigid body+Failure modes

ˆ ( )i iA Au N aa ac=GH

x(Superposition) (Domain decomposition)

0

50

100

150

200

250

300

0 0.0001 0.0002 0.0003 0.0004

Time (s)

Velo

city

of Im

pact

or (m

/s)

Global Enrichment (metals)Global Enrichment (metals)3D simulations3D simulations

DH36 & ERC (3D-21 layers)

MEPU

DH36 & ERC (Shell)

Local Enrichment (metals)Local Enrichment (metals)(in progress)(in progress)

Calculate discontinuity direction at each Gauss point Calculate discontinuity direction at each Gauss point

Align the RVE local coordinate system with one of the Align the RVE local coordinate system with one of the axis normal to the localization planeaxis normal to the localization planeDevelop a 3-point RVE model as follows:Develop a 3-point RVE model as follows:

det 0T n Dn

1

2

3

4

6

78

5

Shell

n

RVEDiscontinuity plane

Gauss point

Constrained RGB

Constrained

periodicity

master

Impact Fragmentation of compositesImpact Fragmentation of composites PhenomenologicalPhenomenological

AdvantagesAdvantages- FastFast

DisadvantagesDisadvantages- ReliabilityReliability- Experiments architectureExperiments architecture dependentdependent

Eigendeformation-based Reduced Order HomogenizationEigendeformation-based Reduced Order Homogenization

Component

Material

Point

Direct HomogenizationDirect Homogenization

AdvantagesAdvantages- ReliabilityReliability- Architecture independent Exp.Architecture independent Exp.

DisadvantagesDisadvantages- Computationally formidableComputationally formidable

Matrix point (s)

Fiber point (s)

Interface point (s)Engineering AccuracyEngineering AccuracyFastFastArchitecture independent Architecture independent ExperimentsExperiments

Validation: Tube Crush ExperimentValidation: Tube Crush ExperimentExperiments by Oak Ridge (Starbuck Experiments by Oak Ridge (Starbuck et al.et al.))Impact Velocity: 4000 mm/secImpact Velocity: 4000 mm/secMicrostructure: Woven compositeMicrostructure: Woven composite

Model Validation (composites)Model Validation (composites)