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VEM × バイオフィルム力学 — 任意多角形/多面体メッシュによるバイオフィルムの機械的解析
Repository: keisuke58/VirtualElementMethods
VEM (Virtual Element Method) は FEM の一般化で、任意多角形/多面体要素上で弾性問題を解ける。形状関数を明示構成しない ("virtual") 代わりに射影演算子で剛性行列を近似する。
| Step | FEM (traditional, 5-step) | VEM (2-step) |
|---|---|---|
| 1 | Confocal z-stack | Confocal z-stack |
| 2 | Voxel segmentation | Colony centroids → Voronoi |
| 3 | Marching cubes | VEM solve ← done! |
| 4 | Tetrahedral remeshing | — |
| 5 | Abaqus FEM solve | — |
| File | Description |
|---|---|
vem.py |
2D Poisson (Sutton 2017 base) |
vem_elasticity.py |
2D plane-stress elasticity (patch test 1e-18) |
vem_3d.py |
3D elasticity on polyhedra (patch test 1e-19) |
vem_3d_advanced.py |
3D Voronoi + sparse solver + VTK export |
vem_apple.py |
Apple-shaped Voronoi demo |
| File | Idea |
|---|---|
vem_spacetime.py |
Space-Time VEM: anisotropic (x,t) Voronoi, SLS 粘弾性 |
vem_growth_coupled.py |
Growth-Coupled VEM: 5-species replicator + VEM + cell division |
vem_confocal_pipeline.py |
Confocal → VEM: 5ch confocal → Voronoi → VEM (2-step) |
vem_phase_field.py |
Phase-field VEM: Aldakheel 2018 style 破壊, DI→G_c |
vem_nonlinear.py |
Neo-Hookean VEM: 大変形超弾性, Newton-Raphson |
vem_error_estimator.py |
A posteriori error: ZZ-type, Dörfler marking |
process_heine_fish.py |
Heine 2025 FISH: real image → VEM |
| File | Purpose |
|---|---|
pipeline_3d_real.py |
3D TIFF → colony segment → Voronoi → VEM |
benchmark_3d_vem_vs_tet.py |
VEM Voronoi vs FEM tet comparison |
phase_field_real_3d.py |
Phase-field fracture on real SAPA biofilm |
vem_phase_field_3d.py |
3D Phase-field VEM on polyhedral mesh (NEW) |
| Metric | Value |
|---|---|
| E range | 10–1000 Pa (literature: 20–14,000 Pa) |
| E ratio CS/DS | up to 28× |
| Convergence L² | 2.14 (Voronoi) |
| 3D Real PA | 65 cells, E 42–237 Pa |
| 3D Real SAPA | 131 cells, DI 0.18–0.79, E 74–682 Pa |
| Phase-field 2D | 69 elements, d_max=0.85, 57/82 cracked |
| Phase-field 3D | 208 polyhedra, catastrophic at step 14, d_max=0.56 pre-cat |
| Tests | 70 passing |
- Phase-Field Fracture — 亀裂力学の概念 + synthetic/real 結果
- Growth-Coupled VEM — 5-species replicator + two-way coupling
- 3D Real Biofilm — Zenodo TIFF → 3D Voronoi → VEM
- Results Gallery — 全結果画像 (~70 images)
- TMCMC 論文 wiki — TMCMC/FEM 側
- Aldakheel et al. (2018) — Phase-field VEM (IKM)
- Wriggers et al. (2024) — VEM textbook