A PCA (Principle Component Analysis)-based microstructure descriptor is proposed in this paper. The PCA process is performed on the microstructures of the material database, and is able to maintain the dominant geometric features using a small number of PCA basis. Moreover, this PCA-based descriptor also gives a closed-form expression between the microstructures within the design space and their physical properties. Previous approaches, for example, based on meta-modeling, involve much more expensive off-line finite element computations. Using this novel PCA-based descriptor, an approach to design a microstructure of optimal physical performance is proposed, taking the concrete case of linear elasticity analysis for demonstration.

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