3D Materials AI / Topological Data Analysis
3D Topology-Aware Microstructure Screening Platform
Generate, upload, visualize, and rank 3D two-phase microstructures with morphology and topological descriptors before expensive FEM, CFD, or fabrication simulations.
3D Microstructure Viewer
Rotatable solid-surface preview
Drag to rotate. Surface faces are shaded with a fixed overhead light.
54%
Solid Volume
phase occupancy
3
β₀ Components
solid connected regions
307
β₁ Tunnels
loops through solid phase
0
β₂ Voids
enclosed pore regions
-304
Euler χ
β₀ − β₁ + β₂
0.209
Surface Density
interface density estimate
Descriptor Interpretation
This candidate has Euler characteristic χ = -304 (β₀ = 3 solid components, β₁ = 307 tunnels, β₂ = 0 enclosed voids). It occupies 54% solid volume with 3 through-connected axises. For the transport objective, it is best described as multi-axis connectivity with balanced porosity.
Suggested next design move: Candidate is ready for downstream FEM/CFD-style simulation screening.
Topological Phase Diagram
Betti numbers and Euler characteristic computed across all thresholds. Each curve is normalized to its own maximum. The dashed line marks the applied threshold.
Percolation
t = 0.43
Solid loses full connectivity above this threshold. Below it: bicontinuous. Above: fragmented islands.
Peak β₁
t = 0.47
Maximum tunnel density (310 loops). Best threshold for transport-optimized metamaterials — highest permeability proxy.
β₂ Onset
t = 0.43
Enclosed pore regions first appear. Below this threshold the solid traps void — relevant for closed-cell foams.
Spatial Correlation & Hyperuniformity
The two-point correlation S₂(r) measures the probability that two points separated by distance r are both in the solid phase. The structure factor S(k) is its Fourier transform; hyperuniform materials exhibit S(k→0)→0, suppressing large-scale density fluctuations—a key design target for phononic metamaterials.
Two-Point Correlation S₂(r) / φ̄²
Correlation length ξ ≈ 1 voxels — distance at which correlations decay to halfway between peak and long-range limit.
Radial Structure Factor S(k) — log scale
Volume fraction φ̄
0.536
S₂(0) = φ̄ = 0.536
Correlation length ξ
1 vx
Characteristic microstructural length scale
Hyperuniformity
Not detected
S(k→0) suppressed vs bulk S(k)
Design To Additive Manufacturing Screening
Morphology descriptors and topology checks provide an early feasibility gate for microstructure designs before expensive simulation, fabrication, or inverse design refinement.
Design
Candidate 3D microstructure generated or uploaded as a thresholded two-phase volume.
Topology Gate
Additive Manufacturing
Ranked candidate prepared for downstream FEM/CFD simulation, printability checks, or inverse design refinement.
Screen Candidate Microstructures
Rank generated 3D candidates with descriptor-based pre-screening objectives. The highest-scoring structures are selected for downstream simulation pipelines.
Method Summary
The workflow combines 3D volume handling, microstructure descriptor extraction, topology-aware screening, spatial correlation analysis, and candidate interpretation before expensive simulation or additive manufacturing steps.