Topology-Aware Blending Method for Implicit Heterogeneous Porous Model Design

TL;DR

This work addresses blending heterogeneous porous models by introducing a topology-aware blending method that mitigates topological errors in blended regions. It proposes an initialization strategy tailored to regions of varying complexity, and formulates topological-error elimination as a persistent-homology-based optimization problem. Through iterative updates of control coefficients, the method produces a blended porous structure that preserves outside-region details while shaping the blending region. The results demonstrate avoidance of topological errors and controlled blending geometry, with potential applications in biomimetics and the design of high-stiffness heterogeneous mechanical models.

Abstract

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.