Modelling feasibility constraints for materials design: Application to inverse crystallographic texture problem

Abstract

The cornerstone of materials design is solving materials-related optimization problems to obtain microstructural or processing variables that lead to the most desirable material properties. Because the objective of materials design is to maximize their performance, the related optimization problems often require a global solution. This type of unconstrained optimization overlooks the feasibility of the solution, which is a key engineering issue. For any practical application, feasibility should be reflected in the constraints included in the optimization problems. Nevertheless, the constraints related to feasibility are considerably complex due to the high dimensionality of the design space and non-physical aspects of the constraints, such as machine specifications, material dimensions, and available initial microstructure. In this work, we propose the use of a simple support vector machine (SVM) trained with information in an existing database to model complex feasibility constraints for material optimization. We present a problem involving optimization of the initial texture of a body-centered cubic (BCC) polycrystalline material to obtain specific target textures after cold-rolling. Both unconstrained and constrained optimizations are conducted for comparison, and the results demonstrate that constrained optimizations yield viable solutions while unconstrained optimizations do not.