Introduction Flexible and stretchable electronics have attracted much attention due to their potential applications in wearable devices, robotics, and healthcare. Among various materials, barium titanate (BTO) is a promising candidate for flexible and stretchable electronics because of its high dielectric constant, piezoelectric property, and superior thermal stability. However, the brittle nature of BTO restricts its application in flexible and stretchable devices. Polymer composites such as polydimethylsiloxane (PDMS) can be used, providing a flexibility and a stretchability for BTO-based devices. In this paper, flexible BTO/PDMS composites with a hierarchical microstructure were prepared and their dielectric performance was optimized. The hierarchical microstructure could enhance the mechanical properties, electrical conductivity, and dielectric performance of the composites. This study could provide valuable insights into the design and fabrication of flexible and stretchable electronic devices based on BTO/PDMS composites.Methods A piece of foam nickel was prepared, cleaned with acetone under ultrasound for 10 min and then washed with deionized water for several times to remove impurities on the surface. An isopropanol was used as a solvent, an appropriate amount of phenolic resin was used as a stabilizer, and an appropriate amount of aluminum nitrate nonahydrate was added to make the BTO positively charged. Little precipitation occurred after mechanical stirring and ultrasonic treatment. A uniform and stable barium titanate suspension was formed. A layer of BTO coating was deposited on the pore walls of the pretreated foam nickel by an electrophoretic deposition (EPD) process. Two copper plates were used as the poles of the electrophoretic deposition. A nickel metal foam template was fixed on a negative pole, immersing it into the EPD tank with the stable BTO suspension To prepare the samples with different BaTiO3 contents, the diameter of the BTO framework pore was controlled via adjusting the electrophoresis time. The sample was sintered in an argon atmosphere at 1 200 ℃ for 2 h, and then immersed in a 1 mol/L FeCl3 solution to completely remove the foam nickel. Finally, the sample was sintered in air at 700 ℃ for 2 h to remove carbon, forming a BTO framework. To determine the mass fraction of BTO, a barium titanate framework was weighed before and after penetration by epoxy resin. The PDMS (with curing agent) was filled into the porous structure and cured at room temperature for 24 h to obtain the BTO/PDMS dielectric composite material. Results and discussion The results indicate that when the BTO content reaches 10.16% (in mass), the relative permittivity of the composite increases up to 85 at 1 000 Hz (compared to only 2.75 for pristine PDMS). Also, the dielectric permittivity increases as the mass fraction of BTO increases from 5% to 20% (in mass). For the BTO with an ordered morphology, the dielectric permittivity value increases, improving the dielectric strength performance in specific directions. Adding PVDF slightly increases the dielectric permittivity, while reducing the difference between the dielectric properties of filler and substrate, thereby enhancing the dielectric strength performance via combining PVDF with PDMS to form a core-shell structure and optimizing the dielectric properties by a finite element method. The hierarchical microstructure of the composites plays an important role in enhancing the dielectric properties. The uniform distribution of BTO particles and the interconnected porous structure of PDMS matrix provide a continuous path for the movement of charge carriers, which contributes to a high dielectric constant and a low dielectric loss of the composites. In addition, the flexible nature of PDMS matrix also makes the BTO/PDMS composites suitable for various applications, such as flexible electronic devices, sensors, and actuators.Conclusions The BTO/PDMS flexible dielectric composites with a hierarchical microstructure were prepared by a template method and an electrophoresis deposition method with BTO as a filling material and PDMS as a matrix. The influences of filler morphology and content on the dielectric constant and dielectric strength of the composites were investigated via finite element simulation analysis. Two kinds of ordered network structures of the composites, i.e., tetrahedral network structure and honeycomb network structure, were designed. This provides a theoretical guidance for the preparation of high-quality dielectric composite materials with superior energy storage density. The main conclusions were as follows: (1) Compared to the particle-filled composites, the BTO/PDMS composites with a hierarchical microstructure have an improved dielectric constant at a low filler content. For instance, the relative dielectric constant of the sample with 10.16% BTO could reach 85 at 1 kHz, which was 31 times higher than that of pure PDMS; (2) The morphology of filler had an impact on the dielectric performance of composites. In the case of a low filler content, the composites with a hierarchical microstructure had a higher dielectric constant rather than those with a solid network structure; (3) PVDF was used to form a nuclear shell structure (PVDF@BTO/PDMS) to improve the relative dielectric constant of the composites to a limited extent and the breakdown performance of composites; (4) The orderly network structures were designed. The ordered network structures with a tetrahedral network structure and a honeycomb network structure could improve the dielectric constant of composites to a certain extent and had the anisotropic characteristics.