MULTI-SCALE PROCESS DESIGN Modeling processes with uncertainty

1. MULTI-SCALE PROCESS DESIGNModeling 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 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 14 12 10 Load (N) 8 6 Mean Possible variations Modeling constitutive response of BCC Ta 4 2 0 0 0.2 0.4 0.6 0.8 Displacement (mm) Tension test modeled using spectral stochastic FEM with uncertain material state Multi-length scale forging AFOSR Grant Number: FA9550-04-1-0070 (Computational Mathematics)PI: Prof. Nicholas Zabaras

2. MULTI-SCALE PROCESS DESIGNStatistical learning for materials-by-design DATABASE OF ODFs Statistical learning z-axis <110> fiber (BB’) Higher dimensional feature space f(x) <k>=15.5431 <k2>=252.71 Desired property distribution 145.4 Initial Optimal (reduced order) 145.2 Reconstruction given limited information about number of grain faces 145 144.8 Probability Youngs Modulus (GPa) 144.6 144.4 144.2 144 143.8 143.6 0 10 20 30 40 50 60 70 80 90 Angle from the rolling direction No. of faces(k) Texture features: Orientation fibers Information theoretic methods Informa- tion filter 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 ? MAXENT: Information theoretic method to obtain entire statistical distribution from incomplete information. Process design for desired properties Stage: 1 Shear Database Model Reduction Classification Stage: 2 Tension Gradient based optimization AFOSR Grant Number: FA9550-04-1-0070 (Computational Mathematics)PI: Prof. Nicholas Zabaras