Detailed Vehicle Collision Simulation
Theory and Physics
Vehicle Collision Simulation
Professor, car crash safety can't be designed without FEM, right?
Exactly. In modern automotive development, hundreds to thousands of FEM simulations are performed before actual vehicle crash tests. FEM leads the design of crash safety.
Collision Classification
| Collision Type | Standard | Speed | Characteristics |
|---|---|---|---|
| Full Frontal (Full Overlap) | FMVSS 208, Euro NCAP | 56 km/h | Full-width rigid barrier impact |
| Frontal Offset | Euro NCAP, IIHS | 64 km/h | 40% offset ODB |
| Side Impact | FMVSS 214, Euro NCAP | 50 km/h | Deformable barrier side impact |
| Rear Impact | FMVSS 301 | 80 km/h | Fuel leakage prevention |
| Pole Side Impact | Euro NCAP | 32 km/h | Narrow obstacles like utility poles |
| Pedestrian Protection | Euro NCAP | — | Head impact on hood |
There are that many collision patterns?
For a single vehicle model, 20 to 50 collision cases are simulated. Each case involves an explicit dynamic calculation of a full-vehicle model with millions of elements for 50 to 200 ms. The computational resources required are enormous.
FEM Model Scale
Typical full-vehicle crash model:
| Item | Value |
|---|---|
| Number of Elements | 3 million to 10 million |
| Number of Nodes | 1 million to 5 million |
| Number of Material Models | 50 to 200 |
| Number of Contact Definitions | Hundreds |
| Calculation Time | 4 to 24 hours (100 to 200 CPUs) |
| Result File Size | 10 to 100 GB |
10 million elements! That's an incredible scale.
It includes everything: BIW (Body-in-White), closures, chassis, powertrain, interior, seats, dummy, airbag... Mesh generation can take weeks, and calculation setup can take days.
Crash Safety Design Philosophy
Energy absorption is the fundamental concept of crash safety:
1. Front Crush Zone — Absorbs energy through controlled buckling
2. Cabin (Occupant Compartment) — High-rigidity cage that does not deform
3. Restraint System — Decelerates occupants with seat belts and airbags
The core of the design is "parts that should crush" and "parts that must not crush," right?
FEM simulates this "controlled buckling." The shape, thickness, and material of the crash box ribs are optimized using FEM to achieve the target energy absorption and deceleration pulse.
Summary
Key Points:
- 20 to 50 collision cases simulated with FEM — Before physical vehicle tests
- 3 million to 10 million element full-vehicle model — LS-DYNA explicit method
- Energy absorption and occupant compartment deformation limitation — Crash safety design philosophy
- Controlled buckling of crash boxes — Optimized with FEM
- Compliance with standards like Euro NCAP, FMVSS — Multiple scenarios
Crash Safety Engineering was Founded by Hugh DeHaven
Hugh DeHaven, considered the father of modern crash safety engineering, proposed the concept of a "variable crash zone" in 1942. The idea of intentionally deforming the engine compartment to absorb energy and protect the passenger cabin during a vehicle collision with an obstacle is the prototype for the crushable zone design implemented in all modern vehicles. Ford's first adoption of DeHaven's theory in a mass-produced vehicle, the padded dashboard in 1956, also stems from the same concept.
Physical Meaning of Each Term
- Inertia Term (Mass Term): $\rho \ddot{u}$, i.e., "mass × acceleration". Have you ever experienced being thrown forward during sudden braking? That "feeling of being pulled" is precisely the inertial force. Heavier objects are harder to set in motion and harder to stop once moving. Buildings shake during earthquakes because the ground moves suddenly while the building's mass "gets left behind." In static analysis, this term is set to zero, which is the assumption that "acceleration can be ignored because force is applied slowly." It absolutely cannot be omitted for impact loads or vibration problems.
- Stiffness Term (Elastic Restoring Force): $Ku$ or $\nabla \cdot \sigma$. When you stretch a spring, you feel a "force trying to return it," right? That is Hooke's law $F=kx$, the essence of the stiffness term. So here's a question—if you pull an iron rod and a rubber band with the same force, which stretches more? Obviously the rubber band. This "resistance to stretching" is the Young's modulus $E$, which determines stiffness. A common misconception: "high stiffness = strong" is incorrect. Stiffness is "resistance to deformation," strength is "resistance to failure"—they are different concepts.
- External Force Term (Load Term): Body force $f_b$ (e.g., gravity) and surface force $f_s$ (pressure, contact force, etc.). Think of it this way—the weight of a truck on a bridge is a "force acting on the entire volume" (body force), while the force of the tires pushing on the road is a "force acting only on the surface" (surface force). Wind pressure, water pressure, bolt tightening force... all are external forces. A common mistake here: getting the load direction wrong. Intending "tension" but it becomes "compression"—sounds like a joke, but it actually happens when coordinate systems are rotated in 3D space.
- Damping Term: Rayleigh damping $C\dot{u} = (\alpha M + \beta K)\dot{u}$. Try plucking a guitar string. Does the sound continue forever? No, it gradually fades away. That's because the vibration energy is converted to heat by air resistance and internal friction in the string. Car shock absorbers work on the same principle—intentionally absorbing vibration energy to improve ride comfort. What if damping were zero? Buildings would keep shaking forever after an earthquake. Since that doesn't happen in reality, setting appropriate damping is crucial.
Assumptions and Applicability Limits
- Continuum Assumption: Treats material as a continuous medium, ignoring microscopic heterogeneity
- Small Deformation Assumption (for linear analysis): Deformation is sufficiently small compared to initial dimensions, stress-strain relationship is linear
- Isotropic Material (unless specified otherwise): Material properties are independent of direction (anisotropic materials require separate tensor definition)
- Quasi-Static Assumption (for static analysis): Ignores inertial and damping forces, considers only equilibrium between external and internal forces
- Non-applicable Cases: Large deformation/large rotation problems require geometric nonlinearity. Nonlinear material behavior like plasticity and creep requires constitutive law extension
Dimensional Analysis and Unit Systems
| Variable | SI Unit | Notes / Conversion Memo |
|---|---|---|
| Displacement $u$ | m (meter) | When inputting in mm, unify loads and elastic modulus to MPa/N system |
| Stress $\sigma$ | Pa (Pascal) = N/m² | MPa = 10⁶ Pa. Be careful of unit system inconsistency when comparing with yield stress |
| Strain $\varepsilon$ | Dimensionless (m/m) | Note the distinction between engineering strain and logarithmic strain (for large deformation) |
| Elastic Modulus $E$ | Pa | Steel: ~210 GPa, Aluminum: ~70 GPa. Note temperature dependence |
| Density $\rho$ | kg/m³ | In mm system: tonne/mm³ (= 10⁻⁹ tonne/mm³ for steel) |
| Force $F$ | N (Newton) | Unify as N in mm system, N in m system |
Numerical Methods and Implementation
FEM for Collision Simulation
Please tell me the technical details of collision simulation.
Element Types
- BIW (Body) — Shell elements (mainly Quad4, HEX8R)
- Closures — Shell elements
- Bumper, Side Members — Shell + Solid
- Dummy — Shell + Solid + 1D elements (joints)
- Airbag — Shell elements + Gas model (ALE/CPM)
Material Models
- Steel Sheet — MAT24 (Elasto-Plastic) + Strain rate dependence (Cowper-Symonds)
- Aluminum — MAT24 or MAT125
- Resin — MAT24 or MAT89
- CFRP — MAT54/58 (Progressive damage)
- Rubber — MAT77 (Ogden hyperelastic)
- Foam — MAT57/63 (Compressible foam)
Strain rate dependence is important, I see.
Strain rate during collision is $10 \sim 1000$ /s. The yield strength of steel increases by 20-50% with strain rate. Ignoring this effect leads to underestimation of energy absorption. Cowper-Symonds law:
Contact
Hundreds of contact definitions are needed in a crash model. LS-DYNA's *CONTACT_AUTOMATIC_GENERAL (global automatic contact) is standard. Prevents penetration using the penalty method.
Summary
The Era Where 10 Million Element Models Solve in 2 Hours
Modern automotive full-vehicle crash models have reached a scale of 7 to 12 million elements, over 5000 material definitions, and over 200 contact pairs. As of 2024, running LS-DYNA MPP on 256 cores (e.g., AMD EPYC 9354 · 128 cores × 2 nodes) completes a 100ms full frontal crash analysis in about 2 to 4 hours. Toyota and VW use a "night run" system where multiple test modes are executed simultaneously overnight, significantly shortening development TAT (Turn Around Time).
Linear Elements (1st Order)
Linear interpolation between nodes. Low computational cost but low stress accuracy. Beware of shear locking (mitigated by reduced integration or B-bar method).
Quadratic Elements (with Mid-nodes)
Can represent curved deformation. Stress accuracy improves significantly, but degrees of freedom increase by about 2-3 times. Recommended: when stress evaluation is critical.
Full Integration vs Reduced Integration
Full Integration: Risk of over-constraint (locking). Reduced Integration: Risk of hourglass mode (zero-energy mode). Choose appropriately for the situation.
Adaptive Mesh
Automatic refinement based on error indicators (e.g., ZZ estimator). Efficiently improves accuracy in stress concentration areas. Includes h-method (element subdivision) and p-method (order increase).
Newton-Raphson Method
Standard method for nonlinear analysis. Updates tangent stiffness matrix each iteration. Achieves quadratic convergence within convergence radius, but computational cost is high.
Modified Newton-Raphson Method
Updates tangent stiffness matrix using initial value or every few iterations. Cost per iteration is low, but convergence speed is linear.
Convergence Criteria
Force residual norm: $||R|| / ||F_{ext}|| < \epsilon$ (typically $\epsilon = 10^{-3}$ to $10^{-6}$). Displacement increment norm: $||\Delta u|| / ||u|| < \epsilon$. Energy norm: $\Delta u \cdot R < \epsilon$
Load Increment Method
Applies full load not all at once, but in small increments. The arc-length method (Riks method) can trace beyond extremum points on the load-displacement curve.
Analogy: Direct Method vs Iterative Method
The direct method is like "solving simultaneous equations accurately with pen and paper"—reliable but takes too long for large-scale problems. The iterative method is like "repeatedly guessing to approach the correct answer"—starts with a rough answer but accuracy improves with each iteration. It's the same principle as looking up a word in a dictionary: it's more efficient to open it at an estimated location and adjust forward/backward (iterative method) than to search sequentially from the first page (direct method).
Relationship Between Mesh Order and Accuracy
1st order elements are like "approximating a curve with a ruler"—represented by straight line segments, so accuracy is limited. 2nd order elements are like a "flexible curve"—can represent curved changes, dramatically improving accuracy even at the same mesh density. However, computational cost per element increases, so judgment should be based on total cost-effectiveness.
Practical Guide
Collision Simulation Practice
Please tell me the workflow for collision simulation.
Workflow
1. Receive CAD Data — Integrate CAD of each component
2. Mesh Generation — Create shell mesh (5-10 mm) with HyperMesh/ANSA
3. Material Definition — Set MAT24, etc., from material test data
4. Modeling of Joints — Spot welds (*CONSTRAINED_SPOTWELD), adhesive, bolts
5. Dummy Placement — Certified dummy models like WorldSID/THOR
6. Restraint System — Seat belts (*ELEMENT_SEATBELT), air
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