Simulated realistic microstructure of SiC particles in Al-alloy matrix Implementation of Real/Simulated 3D Microstructures in FE- Based Computations Arun Gokhale, Georgia Institute of Technology, DMR Volume: 10 6  m 3 Degrees of freedom: > 1 million Quasi-static analysis using ABAQUS/Explicit Constitutive properties Aluminum: Experimental stress-strain curve of Al6061-T6 alloy SiC: Perfectly elastic with E = 410GPa Computations performed at NCSA using TeraGrid Grant DMR070047N Distribution of local max. principal stress Computed stress-strain curves for realistic simulated composites with different SiC volume fractions 3D Mesh generation 30% SiC

Applications to Biological Structures Arun Gokhale, Georgia Institute of Technology, DMR Collaboration with Dr. P. Mouton of National Institute of Aging Left: Traverse of virtual cycloids (light green dots) through different focal planes of thick tissue section of DG in mouse brain The estimated value of the total surface area of the GFAP immunopositive astrocytes per unit vol. of the tissue section =  m 2 /  m 3 V ref for the DG in mouse brain = 1.9 mm 3 Total surface area of GFAP immunopositive astrocytes = 74.1 mm 2 Study of microstructures is central to numerous disciplines where microscopes are used to characterize internal structures. Stereological techniques for quantitative microstructure characterization are becoming increasingly important in all such disciplines due to the thrust towards quantitative description and modeling of the processes and phenomena of interest. Stereological techniques developed in this NSF funded research have also been applied to quantify internal structures in biological tissues including mouse brain.

What is the chance that a randomly placed point in the box will hit a potato in the box? The higher the total amount of potatoes, the higher is the chance/probability. It can be shown that the probability is precisely equal to the ratio of the total volume of the potatoes and the volume of the box, i.e., volume fraction. We can invert this to estimate the volume fraction of the potatoes, or any phase in a microstructure, via experimental estimation of the probability that a randomly placed point lies in the phase of interest. P (Potato) = ? Motivation: SiC particles reinforced Al-alloy composite is structural material useful for aerospace and automotive applications. Its strength and elastic modulus strongly depend on volume fraction of SiC particles. Therefore, it is of interest to estimate volume fraction of SiC. Probability = Average number of grid points contained in SiC divided by the total number of points = P P Volume fraction of SiC = P P Real World Applications of Probability and Statistics 2007 RET Project of High School Teacher Ms. U. Gordon, Clayton County, GA Mentor: Arun Gokhale, Georgia Institute of Technology; Grants: /INT