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MULTI-SCALE PROCESS DESIGN Modeling processes with uncertainty. Robust process models: Modeling uncertainty. 1.5. 1. Standard deviation of Load (N). 0.5. Homogeneous. Heterogeneous. 0. Displacement (mm). 0. 0.2. 0.4. 0.6. 0.8. - PowerPoint PPT Presentation
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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