1

MULTI-SCALE PROCESS DESIGNModeling processes with uncertainty

Research objectives: To develop a mathematically and computationally rigorous gradient-based optimization methodology for virtual multi-length scale robust materials process design that allows the control of microstructure-sensitive material properties

Robust process models: Modeling uncertainty

Multi-length scale

forging

Modeling constitutive response of BCC Ta

AFOSR Grant Number: FA9550-04-1-0070 (Computational Mathematics)PI: Prof. Nicholas Zabaras

0 0.2 0.4 0.6 0.80

2

4

6

8

10

12

14

Displacement (mm)

Lo

ad

(N

)

Mean

0 0.2 0.4 0.6 0.80

0.5

1

1.5

Sta

ndar

d de

viat

ion

of L

oad

(N)

HomogeneousHeterogeneous

Displacement (mm)

Tension test modeled using spectral stochastic FEM with uncertain material state

Possible variations

2

MULTI-SCALE PROCESS DESIGNStatistical learning for materials-by-design

Information theoretic methodsTexture features: Orientation fibers

0 10 20 30 40 50 60 70 80 90143.6

143.8

144

144.2

144.4

144.6

144.8

145

145.2

145.4

Angle from the rolling direction

You

ngs

Mod

ulus

(G

Pa) Desired property distribution

InitialOptimal (reduced order)

Stage: 1 Shear

Stage: 2

Tension

DATABASE OF ODFs

Statistical learning

z-axis <110> fiber

(BB’)

Higher dimensional feature space x

Gradient based optimization

Database

ClassificationModel

Reduction

Process design for desired properties

AFOSR Grant Number: FA9550-04-1-0070 (Computational Mathematics)PI: Prof. Nicholas Zabaras

How much information is required at each scale and what is the acceptable loss of information during upscaling to answer performance related questions

at the macro scale ?

Informa-tionfilter

MAXENT: Information theoretic method to obtain entire statistical distribution from incomplete information.

<k>=15.5431

<k2>=252.71

Pro

babi

lity

No. of faces(k)

Reconstruction given limited

information about number of grain

faces