An open-source Finite Element Method framework in Rust, designed for medical and biomechanical simulation.
ORFAS is a modular FEM framework targeting soft tissue simulation for medical and surgical applications. It is written entirely in Rust and designed around trait-based composability: material laws, element types, solvers, and integrators are all interchangeable without modifying the core assembly pipeline.
The primary domain is biomechanics — passive soft tissue, fiber-reinforced biological structures, and viscoelastic organs — in the tradition of frameworks such as SOFA and FEBio, with a modern memory-safe foundation.
Existing FEM frameworks for medical simulation are predominantly written in C++ (SOFA, FEBio, deal.II). While mature and capable, these frameworks carry significant adoption friction: complex build systems, heavy dependency chains, and architectures designed before modern concurrency and memory safety were first-class language concerns.
Rust offers: memory safety without a garbage collector, zero-cost abstractions, a world-class package manager (Cargo), and a trait system that enables generic programming with compile-time guarantees. In simulation code, where subtle memory bugs and performance regressions are costly, these properties translate directly into correctness and maintainability.
SOFA is the reference framework for medical simulation and the direct inspiration for ORFAS. Its C++ plugin architecture presents a high integration barrier for projects seeking a modern, memory-safe foundation and a simpler contribution model.
Fenris is the most mature FEM library in the Rust ecosystem. Its focus is solid mechanics for computer graphics, and it has been inactive since 2022. ORFAS targets medical simulation and a different design philosophy: full replaceability of every numerical component via traits, and a calibrated tissue library grounded in the biomechanics literature.
- Static and dynamic (implicit Euler) nonlinear FEM on tetrahedral and hexahedral meshes
- Newton-Raphson and Newton-Raphson with cached tangent
- Sparse solvers with ILU(0)-preconditioned conjugate gradient
- Parallel sparse assembly via Rayon (~10x speedup on large meshes)
- Rayleigh damping
- Generic element abstraction —
FiniteElementtrait,Assembler<E>generic over element type,DofTypetrait (Vec3Dof,Vec6Dof) - Tet4 — linear tetrahedron, 1 Gauss point, constant strain
- Tet10 — quadratic tetrahedron, 4-point Keast quadrature, reduces shear locking
- Hex8 — trilinear hexahedron, 2×2×2 Gauss quadrature, structured mesh generator
- Beam2 — Euler-Bernoulli 3D beam, 6 DOF/node, analytical stiffness, circular cross-section
- Shell4 — MITC4 shell (Bathe & Dvorkin 1986), 6 DOF/node, locking-free, fictitious drilling spring
- Non-zero Dirichlet BCs — prescribed displacement values via
FixedNode::all_with_value
| Element | Nodes | DOF/node | Gauss points | Locking | Notes |
|---|---|---|---|---|---|
Tet4 |
4 | 3 | 1 | Yes (~14% bending) | Linear, constant strain |
Tet10 |
10 | 3 | 4 (Keast) | Reduced | Quadratic, validated against basix |
Hex8 |
8 | 3 | 8 (2×2×2) | None | Trilinear hexahedron, structured mesh generator |
Beam2 |
2 | 6 | — (analytical) | None | Euler-Bernoulli 3D, circular section |
Shell4 |
4 | 6 | 4 (2×2 mid-surface) | None (MITC) | Bathe & Dvorkin (1986), drilling spring |
Note on Tet10 and structured meshes: Tet10 shows ~20% error on the cantilever bending benchmark with the structured mesh generated by
Mesh::generate. This is a known limitation of structured tetrahedral meshes with alternating orientation — not a bug in the element. Tet10 is designed for unstructured meshes (e.g. from Gmsh). Full validation against unstructured meshes is planned for v0.9.0 when the VTK Tet10 loader is available.
Note on Shell4 (MITC4): The B-matrix formulation is validated for symmetry and patch tests on flat elements. Physics-level validation (Morley skew plate, pinched cylinder, Scordelis-Lo shell) is planned for v0.9.0.
All hyperelastic materials are implemented in the Lagrangian frame with analytical PK2 stress and consistent tangent stiffness tensors.
| Model | Type | Notes |
|---|---|---|
SaintVenantKirchhoff |
Hyperelastic | Linear elastic tangent, nonlinear at large strains |
LinearElastic |
Linear elastic | Small-strain, for patch tests and validation |
NeoHookeanIso |
Isochoric | Flory decoupled, W = μ/2·(Ī₁ − 3) |
MooneyRivlinIso |
Isochoric | W = c₁·(Ī₁ − 3) + c₂·(Ī₂ − 3) |
OgdenIso |
Isochoric | Principal stretch formulation, arbitrary N |
VolumetricLnJ |
Volumetric | W = κ/2·(ln J)² |
VolumetricQuad |
Volumetric | W = κ/2·(J − 1)² |
HolzapfelOgden |
Anisotropic | Fiber-reinforced, exponential strain energy |
ViscoelasticMaterial<I,A,V> |
Viscoelastic | Prony series, Holzapfel & Gasser (2001) |
Any isochoric model composes with any volumetric model via CompressibleMaterial<I, V>.
Anisotropic fiber contributions are added via CompressibleAnisotropicMaterial<I, A, V>.
Viscoelastic dissipation wraps any composition via ViscoelasticMaterial<I, A, V>.
Calibrated material presets for 10 biological tissues, each with literature reference, experimental protocol, and per-parameter confidence intervals.
| Tissue | Model | Reference |
|---|---|---|
| Liver | Neo-Hookean | Nava et al. (2008) |
| Brain grey matter | Mooney-Rivlin | Budday et al. (2017) |
| Brain white matter | Mooney-Rivlin | Budday et al. (2017) |
| Myocardium (passive) | Holzapfel-Ogden | Holzapfel & Ogden (2009) |
| Arterial wall (media) | Holzapfel-Ogden | Holzapfel et al. (2000) |
| Tendon (ground matrix) | Neo-Hookean | Weiss et al. (1996) |
| Ligament (MCL) | Holzapfel-Ogden | Weiss et al. (1996) |
| Skin | Mooney-Rivlin | Groves et al. (2013) |
| Kidney | Neo-Hookean | Nasseri et al. (2002) |
| Prostate | Neo-Hookean | Phipps et al. (2005) |
Presets can be loaded programmatically or from JSON files at runtime. Each preset is validated against thermodynamic consistency checks at compile time.
check_thermodynamic_consistency verifies any MaterialLaw implementation against
8 necessary conditions: zero energy at rest, zero stress at rest, Hooke linearization,
tangent symmetry, non-negative strain energy, small-strain convergence, positive
definiteness, and frame objectivity. Available at runtime for custom materials loaded
from JSON.
Interactive egui viewer with orbit camera, node picking, displacement colormap, material selection (manual parameters or tissue presets), boundary condition editor, and static/dynamic simulation controls.
ORFAS is in pre-alpha. The public API is unstable and subject to change between versions.
- Rust 2024 edition (
rustup update stable) - Cargo (included with Rust)
git clone https://github.com/LLorgeou21/orfas.git
cd orfas
cargo build --releasecargo run --release -p orfas-viewercargo testNumerical validation results are documented in VALIDATION.md.
| Version | Status | Description |
|---|---|---|
| v0.1 | ✅ Done | Static 3D FEM, linear elasticity, tetrahedral mesh, direct solver, basic egui viewer |
| v0.2 | ✅ Done | VTK mesh loading, elimination boundary conditions, per-node forces, interactive node inspector |
| v0.3 | ✅ Done | Dynamic simulation, implicit Euler time integration, Rayleigh damping, MechanicalState |
| v0.4 | ✅ Done | Nonlinear materials (SVK), Newton-Raphson solver, nonlinear implicit Euler, refactored MaterialLaw |
| v0.5 | ✅ Done | Neo-Hookean material, NewtonRaphsonCachedK, viewer refactor, improved camera |
| v0.6.0 | ✅ Done | Performance — sparse solvers (CsrMatrix), conjugate gradient with ILU(0) preconditioner, NewtonRaphsonSparse |
| v0.6.1 | ✅ Done | Performance — parallel sparse assembly (rayon, ~10x speedup), pre-built CSR pattern, SparseAssemblyStrategy trait |
| v0.7.0 | ✅ Done | Materials — isochoric/volumetric split architecture, NeoHookeanIso, MooneyRivlinIso, OgdenIso, VolumetricLnJ, VolumetricQuad |
| v0.7.1 | ✅ Done | Materials — HolzapfelOgden anisotropic fibers, ViscoelasticMaterial (Prony series), MaterialContext/SimulationContext architecture, FiberField, InternalVariables |
| v0.7.2 | ✅ Done | Materials — orfas-tissues preset library with confidence intervals and literature references; thermodynamic consistency checks; viewer UI reorganization |
| v0.8.0 | ✅ Done | Elements — FiniteElement trait, Assembler<E> generic, FemMesh trait, Mesh<N> generic, Tet4 reimplemented, Tet10 quadratic element (4-point Keast), non-zero Dirichlet BCs |
| v0.8.1 | ✅ Done | Elements — DofType trait, Hex8, Beam2 (Euler-Bernoulli 3D), Shell4 (MITC4, Bathe & Dvorkin 1986); element_stiffness analytical path in assembler |
| v0.9.0 | ⬜ Planned | I/O — VTU/VTK export (ParaView), OBJ/STL/MSH import, VTK Tet10 loader |
| v0.9.1 | ⬜ Planned | I/O — .orfas simulation file format (mesh, material, BCs, solver params, ORFAS version hash, results checksum) |
| v0.10.0 | ⬜ Planned | Scientific — SI unit system via uom crate, compile-time unit safety |
| v0.10.1 | ⬜ Planned | Scientific — standardized validation metrics (Hausdorff distance, nodal RMSE, force-displacement curve error) |
| v0.10.2 | ⬜ Planned | Scientific — automated analytical benchmarks with pass/fail reports and convergence curves |
| v0.11.0 | ⬜ Planned | Architecture — stable public trait audit, SimulationPlugin trait, static and dynamic plugin loading |
| v0.11.1 | ⬜ Planned | Architecture — multi-object scene graph, BarycentricMapping, RigidMapping |
| v0.11.2 | ⬜ Planned | Architecture — .orfas format extended for full scene graph serialization |
| v0.12.0 | ⬜ Planned | Rendering — OpenGL/wgpu renderer, separate visual mesh from simulation mesh |
| v0.12.1 | ⬜ Planned | Rendering — shaders, transparency, colormap pipeline, clinician-friendly viewer |
| v0.13.0 | ⬜ Planned | Multi-body — rigid bodies (6 DOF), FEM-rigid coupling |
| v0.13.1 | ⬜ Planned | Multi-body — articulated constraints (revolute, ball-and-socket) |
| v0.14.0 | ⬜ Planned | Contact — broad-phase collision detection (BVH/AABB) |
| v0.14.1 | ⬜ Planned | Contact — LCP formulation, Projected Gauss-Seidel solver, Coulomb friction |
| v0.14.2 | ⬜ Planned | Contact — self-contact (hollow organs, folding soft tissue, brain under compression) |
| v0.14.3 | ⬜ Planned | Contact — tool/mesh contact, surgical instrument interaction, haptic-ready force feedback pipeline |
| v0.15.0 | ⬜ Planned | Reduction — modal decomposition, model order reduction (ROM) |
| v0.15.1 | ⬜ Planned | Reduction — reduced basis methods; prerequisite for real-time and haptic on realistic meshes |
| v0.16.0 | ⬜ Planned | Topology — infrastructure for runtime mesh modification (add/remove elements) |
| v0.16.1 | ⬜ Planned | Topology — real-time cutting with local remeshing, suture simulation |
| v0.17.0 | ⬜ Planned | Inverse — gradient descent and Nelder-Mead parameter identification |
| v0.17.1 | ⬜ Planned | Inverse — Bayesian uncertainty propagation, Monte Carlo, confidence interval maps |
| v0.18.0 | ⬜ Planned | Interfaces — Python bindings via PyO3, numpy-compatible API |
| v0.18.1 | ⬜ Planned | Interfaces — WebAssembly via wasm-bindgen, browser-based simulation |
| v0.18.2 | ⬜ Planned | Interfaces — DICOM/NIfTI import, automated patient-specific meshing from CT/MRI |
| v0.19.0 | ⬜ Planned | Real-time — hard timing constraints (<10ms/frame), adaptive time stepping |
| v0.19.1 | ⬜ Planned | Real-time — 1000Hz haptic loop, force rendering, integration with Geomagic/OpenHaptics |
| v1.0 | ⬜ Planned | Release — stable C ABI, C/C++ FFI bindings, integration as a SOFA plugin, clinical-grade API documentation |
| v1.x | ⬜ Planned | Clinical validation — benchmarks against experimental datasets, patient-specific case studies |
| Project | Language | Focus | Notes |
|---|---|---|---|
| SOFA | C++ | Medical simulation | Primary inspiration for ORFAS |
| FEBio | C++ | Biomechanics | Strong focus on biological tissues |
| Fenris | Rust | Solid mechanics / graphics | Most mature Rust FEM library, inactive since 2022 |
| deal.II | C++ | General FEM | Reference academic FEM library |
| basix | C++/Python | FEniCS element library | Used to validate Tet10 shape functions and gradients |
-
Cheng, J., & Zhang, L. T. (2018). A general approach to derive stress and elasticity tensors for hyperelastic isotropic and anisotropic biomaterials. International Journal of Computational Methods, 15(04). https://doi.org/10.1142/S0219876218500287
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Connolly, S. J., Mackenzie, D., & Gorash, Y. (2019). Isotropic hyperelasticity in principal stretches: explicit elasticity tensors and numerical implementation. Computational Mechanics, 64(5), 1273–1288. https://doi.org/10.1007/s00466-019-01707-1
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Holzapfel, G. A., & Gasser, T. C. (2001). A viscoelastic model for fiber-reinforced composites at finite strains. Computer Methods in Applied Mechanics and Engineering, 190, 4379–4403. https://doi.org/10.1016/S0045-7825(00)00323-6
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Keast, P. (1986). Moderate degree tetrahedral products Gauss quadrature formulas. Computer Methods in Applied Mechanics and Engineering, 55(3), 339–348. https://doi.org/10.1016/0045-7825(86)90059-9
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Zienkiewicz, O. C., & Taylor, R. L. (2000). The Finite Element Method (5th ed.). Butterworth-Heinemann.
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Andersen, L., & Nielsen, S. R. K. (2008). Elastic Beams in Three Dimensions. DCE Lecture Notes No. 23, Aalborg University. — Local stiffness matrix for Beam2 (eq. 1-104 to 1-106).
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Bathe, K. J., & Dvorkin, E. N. (1986). A formulation of general shell elements — the use of mixed interpolation of tensorial components. International Journal for Numerical Methods in Engineering, 22(3), 697–722. https://doi.org/10.1002/nme.1620220605 — MITC4 shell element (Shell4).
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OpenFAST SubDyn Theory Manual, section 6.3.6.3 — Direction cosine matrix for 3D beam local-to-global transformation (Beam2).
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Liver — Nava, A., Mazza, E., Furrer, M., Villiger, P., & Reinhart, W. H. (2008). In vivo mechanical characterization of human liver. Medical Image Analysis, 12(2), 203–216. https://doi.org/10.1016/j.media.2007.09.001
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Brain (grey and white matter) — Budday, S., Nay, R., de Rooij, R., Steinmann, P., Wyrobek, T., Ovaert, T. C., & Kuhl, E. (2017). Mechanical properties of gray and white matter brain tissue by indentation. Acta Biomaterialia, 48, 319–330. https://doi.org/10.1016/j.actbio.2016.10.036
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Myocardium (passive) — Holzapfel, G. A., & Ogden, R. W. (2009). Constitutive modelling of passive myocardium: a structurally based framework for material characterization. Philosophical Transactions of the Royal Society A, 367, 3445–3475. https://doi.org/10.1098/rsta.2009.0091
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Arterial wall (media) — Holzapfel, G. A., Gasser, T. C., & Ogden, R. W. (2000). A new constitutive framework for arterial wall mechanics and a comparative study with other models. Journal of Elasticity, 61, 1–48. https://doi.org/10.1023/A:1010835316564
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Tendon and ligament (MCL) — Weiss, J. A., Maker, B. N., & Govindjee, S. (1996). Finite element implementation of incompressible, transversely isotropic hyperelasticity. Computer Methods in Applied Mechanics and Engineering, 135(1–2), 107–128. https://doi.org/10.1016/0045-7825(95)00931-0
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Skin — Groves, R. B., Coulman, S. A., Birchall, J. C., & Evans, S. L. (2013). An anisotropic, hyperelastic model for skin: experimental measurements, finite element modelling and identification of parameters for human and murine skin. Journal of the Mechanical Behavior of Biomedical Materials, 18, 167–180. https://doi.org/10.1016/j.jmbbm.2012.10.021
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Kidney — Nasseri, S., Bilston, L. E., & Phan-Thien, N. (2002). Viscoelastic properties of pig kidney in shear, experimental results and modelling. Rheologica Acta, 41(1–2), 180–192. https://doi.org/10.1007/s00397-002-0233-2
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Prostate — Phipps, S., Yang, T. H. J., Habib, F. K., Reuben, R. L., & McNeill, S. A. (2005). Measurement of the mechanical properties of the prostate. Journal of Biomechanics, 38(8), 1733–1741. https://doi.org/10.1016/j.jbiomech.2004.07.028
ORFAS is distributed under the terms of the Apache License, Version 2.0.
See DEVELOPER.md for architecture details, code conventions, and contribution guides.
Developed by LLorgeou21.