Stochastic porous structures are ubiquitous in natural phenomena and have gained considerable traction across diverse domains owing to their exceptional physical properties. The recent surge in interest in microstructures can be attributed to their impressive attributes, such as a high strength-to-weight ratio, isotropic elasticity, and bio-inspired design principles. Notwithstanding, extant stochastic structures are predominantly generated via procedural modeling techniques, which present notable difficulties in representing geometric microstructures with periodic boundaries, thereby leading to intricate simulations and computational overhead. In this manuscript, we introduce an innovative method for designing stochastic microstructures that guarantees the periodicity of each microstructure unit to facilitate homogenization. We conceptualize each pore and the interconnecting tunnel between proximate pores as Gaussian kernels and leverage a modified version of the minimum spanning tree technique to assure pore connectivity. We harness the dart-throwing strategy to stochastically produce pore locations, tailoring the distribution law to enforce boundary periodicity. We subsequently employ the level-set technique to extract the stochastic microstructures. Conclusively, we adopt Wang tile rules to amplify the stochasticity at the boundary of the microstructure unit, concurrently preserving periodicity constraints among units. Our methodology offers facile parametric control of the designed stochastic microstructures. Experimental outcomes on 3D models manifest the superior isotropy and energy absorption performance of the stochastic porous microstructures. We further corroborate the efficacy of our modeling strategy through simulations of mechanical properties and empirical experiments.

翻译：随机多孔结构普遍存在于自然现象中，并因其卓越的物理特性而在各个领域受到广泛关注。近年来对微观结构兴趣的激增源于其令人瞩目的特性，例如高强重比、各向同性弹性以及仿生设计原理。然而，现有随机结构主要采用过程建模技术生成，这在表征具有周期性边界的几何微观结构方面存在显著困难，进而导致复杂的模拟和计算开销。本文提出一种创新的随机微观结构设计方法，确保每个微观结构单元的周期性以促进均质化。我们将每个孔隙及邻近孔隙间的互联隧道概念化为高斯核，并利用最小生成树技术的改进版本以保证孔隙连通性。通过飞镖投掷策略随机生成孔隙位置，并定制分布规律以强制实现边界周期性。随后采用水平集方法提取随机微观结构。最后，运用Wang瓦片规则增强微观结构单元边界的随机性，同时保持单元间的周期性约束。该方法实现了对所设计随机微观结构的便捷参数化控制。三维模型实验结果表明，随机多孔微观结构具有优异的各向同性和能量吸收性能。我们进一步通过力学性能仿真和实验验证了建模策略的有效性。