Structure Identification and Compression Behavior Analysis of 3D Fibrous Networks via Persistent Homology

Abstract

Three-dimensional fibrous networks combine high porosity with a characteristic nonlinear J-shaped compressive response, yet the topological origins of this stiffening behavior remain elusive due to the complexity of their random architecture. Here we investigate the structural mechanism governing this response by integrating persistent homology (PH) analysis of X-ray computed tomography images with image-based finite element modeling. We demonstrate that persistent homology efficiently identifies fiber contact points and Side-by-side fused regions from tomographic images, enabling construction of a topology-faithful finite element model that successfully reproduces the J-shaped compressive response. Beyond structural identification, the resulting PH1 loop diameter distribution serves as a phenomenological descriptor of the underlying heterogeneity, qualitatively accounting for the sequential stiffness transition from large, compliant loops to small, stiff ones as compression progresses. This mechanism is corroborated by scaling analysis of the nominal stress-volume fraction relation, which reveals a structural evolution from an initial geometric contact regime (S ∝ϕ3) to a stable bending-dominated regime (S ∝ϕ2). Our findings suggest a topological framework for relating microscopic constraint networks to macroscopic mechanics, providing fundamental design principles for advanced disordered materials.