First-Order Microstructure Sensitive Design Based on Volume Fractions and Elementary Bounds

Prior chapters of this book have focused largely on the experimental aspects of EBSD technique. We shift our attention here to a mathematical framework for establishing invertible linkages between the mesoscale internal structure of the material and the macroscale properties exhibited by the material. It is noted that the current practice in engineering design does not pay adequate attention to the internal structure of the material as a continuous design variable. The design effort is often focused on the optimization of the geometric parameters of the component being designed using robust macroscale numerical simulation tools, while the material selection is typically relegated to a relatively small database. Furthermore, material properties are usually assumed to be isotropic, and this significantly reduces the design space.