| name | impact-analysis |
| description | Impact and crashworthiness analysis — impulse-momentum, energy absorption, crush zones, HIC (head injury criterion), FMVSS standards, explicit FEA (LS-DYNA), strain rate effects, material failure criteria, pedestrian protection, side impact, NCAP. |
| metadata | {"priority":7,"promptSignals":{"phrases":["impact analysis","crashworthiness","crash simulation","energy absorption","HIC head injury","FMVSS crash"],"minScore":3}} |
Impact and Crashworthiness Analysis — Complete Skill
Impact Mechanics Fundamentals
Impulse-momentum theorem:
J = F × Δt = Δp = m × Δv [N·s; J = impulse; Δv = velocity change]
Energy (kinetic): E_k = (1/2) × m × v² [J]
Coefficient of restitution:
e = v_rebound / v_approach [e = 0: perfectly plastic; e = 1: perfectly elastic; real: 0 < e < 1]
For vehicle crash (structural collapse): e ≈ 0 (fully plastic)
Rigid barrier crash (vehicle at v₀):
Conservation of momentum: m × v₀ = (m + M_barrier) × v_f → v_f ≈ 0 (rigid barrier)
Energy dissipated: E = (1/2) × m × v₀² [all KE must be absorbed by crush structure]
Deceleration pulse:
Average deceleration: a_avg = v₀ / t_crush = v₀² / (2 × δ_crush) [m/s²; δ_crush = crush distance]
In g: n = a_avg / 9.81 [higher g = shorter crush = more severe pulse]
Injury Criteria
HIC (Head Injury Criterion)
Head Injury Criterion:
HIC = max over any interval (t₂-t₁): [(t₂-t₁) × (1/(t₂-t₁) × ∫t₁^t₂ a(t) dt)^2.5]
a(t) = head resultant acceleration in g; HIC calculated over any 15 ms or 36 ms window
HIC limits:
FMVSS 208 (frontal crash): HIC ≤ 700 (15 ms window) → associated with 5% serious head injury risk
European ECE-R21: HIC ≤ 1,000 (36 ms window); more lenient
AIS 4+ head injury probability: HIC = 1,000 → ~16% risk; HIC = 700 → ~5%
Alternative: HPC (Head Performance Criterion — Euro NCAP):
Similar to HIC but with linear regression improvement; target HPC ≤ 500 (stricter for pedestrian protection)
Chest and Thorax
Chest deflection criterion:
FMVSS 208: chest deflection ≤ 76 mm (50th percentile male Hybrid III dummy); ≤ 63 mm (female)
Combined thoracic index (CTI): CTI = (A_max/A_int) + (D_max/D_int) ≤ 1.0
Femur load: ≤ 10,000 N (femur force per FMVSS 208 for knee bolster impact)
Neck criteria: Nij (combined neck force and moment criterion); Nij ≤ 1.0 per FMVSS 208
Pedestrian Protection (Euro NCAP TRL method)
Lower leg: legform impactor; max bending angle ≤ 21°; max shear ≤ 6 mm; max acceleration ≤ 200g
Upper leg: adult form; max force ≤ 5 kN; bending moment ≤ 300 N·m
Head: child and adult head form; HPC ≤ 500 (good); ≤ 1,000 (adequate)
FMVSS Crashworthiness Standards
| FMVSS | Test | Speed | Requirement |
|---|
| FMVSS 208 | Frontal ODB (40%) | 56 km/h | HIC ≤ 700; chest ≤ 76 mm; etc. |
| FMVSS 208 | Frontal full barrier | 48 km/h | Same criteria |
| FMVSS 214 | Side pole impact | 32 km/h | Rib displacement; thorax criterion |
| FMVSS 301 | Rear moving barrier | 80 km/h | No fuel spillage |
| FMVSS 216 | Roof crush | 2.5 × vehicle weight | Survive without collapse |
| FMVSS 305 | Post-crash EV | — | No electrolyte spillage |
Euro NCAP (more demanding than FMVSS for most tests):
Full frontal rigid barrier: 50 km/h; ODB (Offset Deformable Barrier): 64 km/h; side MDB: 50 km/h; far-side test: 50 km/h; pole: 29 km/h
Energy Absorption Structure Design
Crush Zone (Front Rail)
Progressive folding (crash box):
Thin-walled square tube under axial compression → Euler column → initial buckling → progressive fold
Mean crush force (Alexander formula):
F_mean = 13.06 × σ_0 × t^1.5 × C^0.5 [N; σ_0 = flow stress; t = wall thickness; C = side length; all in mm for F in N]
Efficiency:
η_crush = F_mean / F_peak [target: > 70% to minimize peak force]
Peak force: initial elastic + plastic collapse → F_peak = 2.0–3.0 × F_mean for sudden collapse
Triggered tubes (notch, emboss): reduce F_peak/F_mean to 1.2–1.5 by controlling fold initiation
Crash box (front energy absorber):
E_absorbed = F_mean × δ_crush [J; δ_crush = available crush stroke]
Required: E_absorbed = (1/2) × m_vehicle × v₀² / N_rails [N_rails = 2 for front crash]
Bending Energy Absorption (Cross-Members)
For side impact: cross-member bends as beam
E = (1/12) × σ_0 × b × t² × L [J; b = width; t = thickness; L = length; bending energy until failure]
B-pillar: designed to be stiff (not absorb energy) → protect occupant space → bending stiffness critical
Material specific energy absorption (SEA):
SEA = E_absorbed / m_structure [J/kg; higher is better for lightweight crashworthiness]
| Material | SEA [kJ/kg] |
|---|
| Mild steel | 10–20 |
| AHSS DP 780 | 20–30 |
| Aluminum 6061 | 25–40 |
| CFRP (UD axial) | 60–120 |
| GFRP | 40–80 |
Explicit FEA for Crash Analysis (LS-DYNA)
Methodology
Explicit time integration:
Δt = C_CFL × min(L_element / c) [CFL stability; L_element = minimum element size; c = wave speed]
For steel: c = √(E/ρ) = √(210×10⁹/7,800) = 5,200 m/s; 5 mm element → Δt ≈ 1 μs
Total simulation time: typically 100–200 ms for frontal crash; 50–100 ms for side impact
Number of time steps: 10⁵–10⁶ → computationally expensive (hours to days on HPC)
Contact formulation:
*CONTACT_AUTOMATIC_SINGLE_SURFACE: handles self-contact (folding sheet metal)
*CONTACT_AUTOMATIC_SURFACE_TO_SURFACE: between distinct parts (panel to panel)
Penalty-based contact; contact stiffness = 0.1 × material stiffness (typical)
Hourglass control:
Shell elements (type 16: Belytschko-Tsay): susceptible to hourglass modes → use IHQ=8 or add bulk viscosity
Solid elements: reduced integration → hourglass; add stiffness-based hourglass control
Material Models
*MAT_024 (MAT_PIECEWISE_LINEAR_PLASTICITY): most common for metal crash
Input: stress-strain curve at multiple strain rates; failure strain (effective plastic strain)
Strain rate effect: LCSS (load curve ID for σ₀ vs. ε̇); Cowper-Symonds:
σ_dynamic = σ_static × (1 + (ε̇/C)^(1/n)) [C = 40 s⁻¹, n = 5 for mild steel; C = 3,200 s⁻¹, n = 5 for Al]
*MAT_054 (MAT_ENHANCED_COMPOSITE_DAMAGE): for CFRP
Chang-Chang failure criteria (fiber tensile/compressive, matrix tensile/compressive)
Progressive damage: SOFT = residual fiber/matrix stiffness after failure
*MAT_020 (MAT_RIGID): barrier, impactor; deformable only at contact interface
Element Types for Crash
Shells (Type 16 — Belytschko-Tsay reduced integration): most efficient; BIW, closures, floor
Minimum 4 elements per fold width → element size 3–7 mm for most body parts
Integration points: 5 through thickness (NIP=5) for bending accuracy in thin sheet
Solids (type 1 — reduced integration 8-noded): foam, rubber, seats
Bulk viscosity: QA=1.5, QB=0.06 (standard for shock wave propagation)
Mass scaling: artificially increase very small elements' density → increase Δt; use with caution (< 5% total mass scaling); check kinetic energy of scaled mass
Strain Rate Effects in Crash
Mild steel: significant strain rate strengthening; flow stress increases 40–100% at ε̇ = 1,000 s⁻¹
AHSS (DP780): smaller strain rate effect (n ≈ 3 in Cowper-Symonds); relative improvement over mild steel at low strain rates reduces at high strain rates
Aluminum: very small strain rate effect (C = 3,200, n = 5 → minimal σ increase at crash rates)
CFRP: nearly rate-independent in fiber direction; matrix sensitive to rate
Practical implication: mild steel crash structures appear better at crash rates than quasi-static; must test at dynamic rates
Occupant Protection Systems
Airbag: inflates in 15–30 ms; Takata/Autoliv/ZF; controlled by accelerometer in ECU; deployment threshold: typically 20–30g average deceleration
Seatbelt pretensioner: fires at crash onset; removes slack; limits occupant excursion
Seatbelt load limiter: allows belt to pay out controlled amount → limits chest load
Dummy selection:
50th male Hybrid III: frontal tests
5th female Hybrid III: different injury sensitivity
WorldSID 50th male: side impact (biofidelic)
THOR (Test Device for Human Occupant Restraint): newer; more biofidelic; Euro NCAP 2020+
Standards
| Standard | Scope |
|---|
| FMVSS 208 | Occupant protection in frontal crash |
| FMVSS 214 | Side impact protection |
| FMVSS 216 | Roof crush resistance |
| Euro NCAP Technical Bulletin | European new car assessment |
| SAE J211 | Instrumentation for impact tests |
| ISO 6487 | Road vehicle measurements in impact tests |
| SAE J2551 | FMVSS 208 dummy positioning |
Output
Provide: crash event (frontal/side/rear/rollover), test standard (FMVSS/Euro NCAP/FMEA), vehicle mass [kg] and crash speed [km/h], energy to dissipate E [kJ], crush zone design (F_mean [kN], crush stroke [mm], efficiency η), HIC calculated (15 ms window) vs. limit (≤ 700 for FMVSS), chest deflection [mm] vs. limit (≤ 76 mm), femur load [kN], LS-DYNA model summary (element count, Δt [μs], run time [ms]), material models used, peak deceleration [g] and duration [ms], injury criteria all pass/fail, and applicable standard (FMVSS 208, Euro NCAP, SAE J211).
