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In the last years, lithium-ion batteries (LIBs) have become the most important energy storage system for consumer electronics, electric vehicles, and smart grids. A LIB is composed of several unit cells. Therefore, one of the most important factors that determine the performance of a LIB are the characteristics of the unit cell. The design of LIB cells is a challenging problem since it involves the evaluation of expensive black-box functions. These functions lack a closed-form expression and require long-running time simulations or expensive physical experiments for their evaluation. Recently, Bayesian optimization has emerged as a powerful gradient-free optimization methodology to solve optimization problems that involve the evaluation of expensive black-box functions. Bayesian optimization has two main components: a probabilistic surrogate model of the black-box function and an acquisition function that guides the optimization.

Structures with multiple materials have now become one of the perceived necessities for automotive industry to address vehicle design requirements such as light-weight, safety, and cost. The objective of this study is to develop a design methodology for multi-material structures accountable for vehicle crash durability. The heuristic topology synthesis approach of Hybrid Cellular Automaton (HCA) framework is implemented to generate multi-material structures with the constraint on the volume fraction of the final design. The HCA framework is integrated with ordered-SIMP (solid isotropic material with penalization) interpolation, artificial material library, as well as statistical analysis of material distribution data to ensure a smooth transition between multiple practical materials during the topology synthesis.