Porous structures are materials consisting of minuscule pores, where the microstructure morphology significantly impacts their macroscopic properties. Integrating different porous structures through a blending method is indispensable to cater to diverse functional regions in heterogeneous models. Previous studies on blending methods for porous structures have mainly focused on controlling the shape of blending regions, yet they have fallen short in effectively addressing topological errors in blended structures. This paper introduces a new blending method that successfully addresses this issue. Initially, a novel initialization method is proposed, which includes distinct strategies for blending regions of varying complexities. Subsequently, we formulate the challenge of eliminating topological errors as an optimization problem based on persistent homology. Through iterative updates of control coefficients, this optimization problem is solved to generate a blended porous structure. Our approach not only avoids topological errors but also governs the shape and positioning of the blending region while remaining unchanged in the structure outside blending region. The experimental outcomes validate the effectiveness of our method in producing high-quality blended porous structures. Furthermore, these results highlight potential applications of our blending method in biomimetics and the design of high-stiffness mechanical heterogeneous models.

翻译：多孔结构是由微小孔隙组成的材料，其微观结构形态显著影响宏观性能。为满足异质模型中不同功能区域的需求，通过混合方法集成不同多孔结构至关重要。以往关于多孔结构混合方法的研究主要集中于控制混合区域的形状，但在有效解决混合结构中的拓扑错误方面仍存在不足。本文提出一种新的混合方法，成功解决了这一问题。首先，我们提出一种新颖的初始化方法，针对不同复杂度的混合区域采用差异化策略。随后，我们将消除拓扑错误的问题构建为基于持续同调的优化问题。通过迭代更新控制系数，求解该优化问题以生成混合多孔结构。我们的方法不仅避免了拓扑错误，还能控制混合区域的形状和位置，同时保持混合区域外的结构不变。实验结果验证了本方法在生成高质量混合多孔结构方面的有效性。此外，这些结果凸显了我们的混合方法在仿生学和高刚度机械异质模型设计中的潜在应用价值。