Statistical Modeling and Simulation for Microstructure in Materials Science

The main accomplishment in this project consists of two parts I Reconstruction cycle in microstructure modeling and II Computation of effective properties via Markov chain Monte Carlo MCMC algorithms. The details are contained in Derr 1998 -- a draft of Ph. D. dissertation entitled Statistical modeling of microstructure with applications to effective property computation in materials science by Bob Derr under the supervision of Chuanshu Ji. One of the most important issues in materials science is the connection between materials properties, e.g., conductivity, elastic moduli, strength, etc. and microstructures. Along this line, many computer models were proposed to generate synthetic microstructures on which some numerical schemes, e.g., finite element, were used to calculate the materials properties of interest, assuming the local properties satisfy certain partial differential equations for stressstrain or diffusions. On the other hand, experimentation was conducted in laboratories which measures those properties from real materials. A significant gap exists between these two aspects of the study due to the lack of methodology for fitting the computer models i.e., estimating the parameters in those models based on the real microstructure data.