Topology-aware blending method for implicit heterogeneous porous model design

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.