impact-analysis

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).