4. Finite element modeling of the human body
A human body model (HBM) is only as trustworthy as the finite element discretization beneath it. Before any injury criterion can be evaluated, the geometry of bones, soft tissue, organs, and membranes must be converted into a mesh whose element types, integration scheme, and contact behavior are appropriate for impact loading. This chapter walks through the four decisions that dominate HBM quality: how the mesh is generated, which element formulations are used, how hourglassing is controlled, and how contact is defined between anatomical parts and between the occupant and the vehicle interior.
Mesh generation: from medical images to a solver-ready model
Most production HBMs originate from computed tomography (CT) and magnetic resonance imaging (MRI) scans of a seated or supine volunteer, or from cadaveric sectioning data. The pipeline is consistent across the THUMS, GHBMC, and SAFER families: segmentation of each anatomical structure, surface extraction, geometric cleanup, volume meshing, and finally assignment of material and element properties. Segmentation quality sets the ceiling for everything downstream — a cortical shell that is 0.5 mm too thick will over-stiffen the rib cage and bias thoracic deflection results.
Surface meshes are typically generated as triangular shells and then filled with tetrahedral or hexahedral volumes. For thin structures such as the skull cortex, ribs, and pelvis cortical shell, a structured hexahedral or wedge-dominant mesh is preferred because it captures bending behavior with fewer elements. For bulky soft tissue — adipose, muscle, brain — tetrahedral meshes are common because they conform to complex organ boundaries. A practical rule of thumb for impact HBMs is an element edge length of 3–5 mm in soft tissue, 1–2 mm in cortical bone, and 0.5–1 mm in brain tissue where strain gradients are steep. Mesh convergence should be checked by refining a region (for example, the rib cage) by a factor of two and confirming that peak deflection and strain change by less than roughly 5%.
Element types and formulations
Impact simulations are explicit, large-deformation problems, so element choice is driven by volumetric locking, shear locking, and hourglassing trade-offs. The table below summarizes the formulations most often used in HBMs.
| Anatomical region | Typical element | Formulation notes |
|---|---|---|
| Cortical bone (skull, ribs, pelvis) | 4-node shell or 8-node solid | Shell with reduced integration and hourglass control; solid hexahedra where thickness permits |
| Trabecular bone | 8-node hexahedron | Reduced integration (1 point) with stiffness-based hourglass control |
| Brain, liver, adipose | 4-node tetrahedron or 8-node hexahedron | Tetrahedra avoid hourglassing but are stiffer in bending; hexahedra need hourglass control |
| Membranes (dura, skin) | 3- or 4-node membrane shell | No bending stiffness; used with membrane formulation |
| Ligaments, tendons | 2-node truss or discrete spring | Tension-only behavior; failure defined by force or strain limit |
| Seat belt, airbag fabric | Membrane shell | Fabric material with orthotropic behavior and strain-rate dependence |
For solid elements, fully integrated hexahedra (2×2×2 Gauss points) are accurate but expensive and prone to volumetric locking in nearly incompressible soft tissue. Reduced-integration hexahedra (1 point) are the workhorse of explicit HBM codes because they are fast and avoid locking, but they are susceptible to zero-energy hourglass modes. Tetrahedra are often fully integrated and hourglass-free, which makes them attractive for brain and organ meshes, at the cost of added stiffness in bending-dominated regions.
Hourglass control
Hourglass modes are non-physical deformation patterns that produce zero strain energy at the integration point. In a reduced-integration hexahedron, the classic pattern is a alternating "bow-tie" displacement of the eight nodes. If uncontrolled, these modes grow without bound and corrupt the solution — you will see mesh distortion that does not correspond to any physical load path, often accompanied by negative volume errors and premature termination.
Two control strategies are common. Stiffness-based hourglass control adds artificial stiffness proportional to the element's elastic moduli; it is the default in many explicit solvers and is appropriate for most HBM soft tissue. Viscous hourglass control adds damping proportional to the hourglass mode velocity; it is useful in highly dynamic events but can over-damp low-frequency response. A practical starting point is a stiffness coefficient of 0.05–0.10 for soft tissue and 0.10 for bone, then verify that the hourglass energy remains below about 5% of the internal energy throughout the run. If hourglass energy exceeds this threshold, refine the mesh locally, switch to a fully integrated formulation in that region, or increase the control coefficient — in that order of preference.
Contact definitions
Contact in an HBM is not a single definition but a hierarchy of interactions: self-contact within a part (for example, folding skin), part-to-part contact between organs and surrounding structures, and occupant-to-environment contact with the seat, belt, airbag, and steering wheel. Explicit solvers typically use penalty-based or kinematic contact algorithms. Penalty contact is robust and allows small penetrations; kinematic contact enforces the constraint more strictly but can introduce noise in force output.
Key parameters to set deliberately include the contact thickness (often equal to the shell thickness for membranes), the penalty stiffness scale factor, and the friction coefficient. For belt-to-clothing contact, a friction coefficient of 0.3–0.5 is typical; for organ-to-organ contact, lower values (0.05–0.2) are used to approximate lubricated sliding. Contact between the occupant and rigid interior parts should use a stiffer penalty to prevent visible penetration, while soft-to-soft contact can use a softer penalty to improve stability.
The figure below summarizes how these four modeling decisions feed into a single impact simulation and where each one most strongly influences the result.
Putting it together: a reproducible check
A useful sanity check before committing to a full impact run is a short "unit" simulation on a single anatomical region. For example, load a rib cage model with a 50 mm rigid impactor at 3 m/s and monitor three quantities: hourglass energy as a fraction of internal energy, the number of negative-volume elements, and the peak rib deflection. If hourglass energy stays below 5%, no elements invert, and the deflection falls within the published corridor for that loading condition, the mesh, element, and hourglass settings are consistent. If hourglass energy spikes, inspect the rib cortical shell first — thin shells with poor aspect ratios are the most common source. If contact forces oscillate, reduce the penalty stiffness or increase the contact thickness slightly.
These four decisions are coupled: a coarse mesh forces larger elements, which in turn makes hourglass control more critical and contact thickness more influential. Treat them as a single calibration problem rather than four independent settings, and document the final values — element size, formulation, hourglass coefficient, penalty scale, and friction — so that the model can be reproduced and audited.