Fabricable stochastic periodic porous microstructures: A Wang cube and Gaussian kernel approach

Abstract

Stochastic porous structures, characterized by randomly distributed voids within solid materials, are prevalent in natural systems such as geological formations, biological tissues, and ecosystems. These structures play crucial roles in processes like nutrient transport and water retention, making them a key focus of interdisciplinary research. Traditional design methods for stochastic porous structures often require detailed modeling of the entire structure, leading to high computational costs. To alleviate this, periodic microstructures are commonly used to fill target regions with repetitive units. However, generating large-scale stochastic porous structures that combine smooth connectivity with global randomness using periodic units remains a significant challenge. This paper presents a novel approach for generating periodic stochastic porous microstructures based on Wang tile rules. The proposed method employs a parameterized generative model with a dual-layer structure, incorporating 27 types of periodic periphery configurations and internal pore-tunnel structures formed from randomly distributed Gaussian kernels. This design balances stochasticity with boundary constraints. Simulations and experiments validate the proposed approach, showing that the resulting stochastic porous microstructures exhibit distinct deformation patterns and superior energy absorption compared to periodic microstructures.