(763h) Initial Investigations in General Optimization-Based Design of Materials

Materials development today remains largely experimental. Techniques such as density functional theory [1] can be used to model material behavior at the quantum level, and other methods such as molecular dynamics [2] or Monte Carlo [3] simulations have also been used to better understand the atomic/molecular scale. However, there remains a gap between the ability to model and probe molecular-level phenomena (even if it can lead to simulation of properties such as shear strength [4]) and to utilize this knowledge in designing materials. One method for finding optimal material designs computationally is process-specific, using relationships between key parameters known to impact the desired properties of a material to model material behavior and then find the optimal parameters for material design given this model (e.g., [5]). A game-changing technology for materials design would be techniques for computationally determining what material design meets required product properties and also is “optimal” (in a sense that may be defined with respect to, for example, cost of manufacture or sustainability) in a general sense that does not pre-suppose relationships between variables specific to a given application domain.

To achieve this goal, the current barriers to success must be clarified and the desired outcomes that are not possible today have to be mathematically formalized so that further work can be performed in rigorously addressing these issues. A framework for addressing optimal materials design is proposed in which an optimization problem is formulated with the squared deviation of a material’s property (e.g., tensile strength) from a target minimized in the objective function, and the decision variables allow the material structure and composition to be selected to obtain a material with properties as close as possible to the targets. A model must be selected to relate these decision variables to the material properties. Different methods for formulating the optimization variables will be explored, as will different modeling techniques. Fundamental limitations for this methodology will be mathematically formalized to elucidate the questions which must be further mathematically treated to allow the proposed method to advance.

[1] D. Sholl and J. A. Steckel. Density Functional Theory: A Practical Introduction. John Wiley & Sons, Hoboken, NJ, 2009.

[2] D. C. Rapaport. The Art of Molecular Dynamics Simulation. Cambridge University Press, Cambridge, UK, second edition, 2004.

[3] D. Frenkel and B. Smit. Understanding Molecular Simulation: From Algorithms to Applications. Academic Press, San Diego, CA, second edition, 2002.

[4] Y. Umeno, A. Kubo and S. Nagao. Density functional theory calculation of ideal strength of SiC and GaN: Effect of multi-axial stress. Computational Materials Science, 109:105-110, 2015.

[5] C. L. Hanselman and C. E. Gounaris. A mathematical optimization framework for the design of nanopatterned surfaces. AIChE Journal, 62:3250-3263, 2016.