  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.
