Data-driven design of three-dimensional periodic piezoelectric structures via high-throughput calculations

• An FFT-based phase field model was developed for high-throughput calculations of electromechanical responses. • The data-driven framework was presented by integrating the FFT-based phase field model and Gaussian process model. • The optimization design of three-dimensional porous structures for piezoelectric composite was investigated. • The optimal structure that comprises a main continuous skeleton and some floating particles was obtained. Cellular materials with porous structures exhibit distinct mechanical and physical properties compared to their solid counterparts. Developing high-performance cellular materials is of great engineering importance. This paper presents a data-driven strategy for the optimal design of three-dimensional (3D) periodic cellular materials, with application to the piezoelectric materials for maximizing the hydrostatic response. The 3D periodic geometry is parameterized using high-order 3D Fourier series, with which a screening of 3D periodic structures with tremendous complexity and variability in shape and morphology is conducted. High-throughput fast-Fourier-transform based piezoelectric simulations are performed in high resolution to handle complicated lattice geometries, yielding a reliable structure-property dataset. A Gaussian-process based surrogate model is then constructed for accelerating the location of optimal 3D piezoceramic structure in the high-dimensional design space. The optimized periodic structure is found to bring in piezocomposite remarkably higher hydrostatic figure of merit (HFOM) than the conventional and recently published alternatives. The high-resolution simulation reveals that such exceptional performance is intimately associated with the presence of floating piezoceramic particles and an optimized continuous lattice skeleton, which collectively contribute to the favorable redistribution of the internal electric displacement field. This study successfully explores the computationally daunting, thus as yet barely studied 3D periodic structures with extreme complexity. It demonstrates the synergistic strength of advanced simulation and data-driven optimization in pushing the boundary of cellular materials performance via deep screening of structure space.