Impact Analysis (Drop and Collision)
Impact Analysis (Drop and Collision): Theoretical Foundations
Fundamentals of Impact Analysis
Professor, how is impact analysis different from regular dynamic analysis?
Impact is a phenomenon where a large force acts over an extremely short time ($\mu s \sim ms$). The time scale is orders of magnitude shorter than that of typical vibration analysis.
Classification of Impact
| Type | Time Scale | Example | Analysis Method |
|---|---|---|---|
| Low-Velocity Impact | 1–100 ms | Drop, Vehicle Collision | Explicit FEM |
| High-Velocity Impact | 0.1–1 ms | Ballistic Impact, Tool Impact | Explicit FEM + SPH |
| Hyper-Velocity Impact | < 0.1 ms | Space Debris, Explosion | SPH, ALE |
| Shock Wave | $\mu s$ | Blast, Underwater Explosion | ALE, Eulerian Method |
So the analysis method changes depending on the time scale.
Low-velocity impact is sufficiently handled by standard explicit FEM. For high-velocity impact, elements undergo large distortion, requiring methods like SPH (Smoothed Particle Hydrodynamics) or ALE.
Mechanics of Impact
Basic impact parameters:
- Impact Velocity $v$ — Kinetic energy $E_k = mv^2/2$
- Impact Duration $\Delta t$ — Time from contact to separation
- Peak Force $F_{max}$ — Maximum value of impact force
- Impulse $I = \int F dt \approx m \Delta v$ — Change in momentum
Can we roughly estimate the impact result using energy conservation?
Assuming all $E_k = mv^2/2$ is converted into deformation energy:
Comparing FEM results with this rough estimate serves as a sanity check.
Impact Analysis in FEM
In explicit FEM:
1. Model the impactor (rigid or deformable body)
2. Model the target (shell/solid + Material Nonlinearity)
3. Define contact (Penalty Method)
4. Set initial velocity
5. Execute time-history analysis
6. Evaluate force-time, deformation-time, energy-time
Summary
Key Points:
- Impact involves large forces over short times — $\mu s \sim ms$ scale
- Explicit FEM is standard — LS-DYNA, Abaqus/Explicit
- SPH/ALE for high-velocity impact — Avoids large element distortion
- Rough estimate check with energy conservation — $E_k = mv^2/2$
- Force-time curve and deformation pattern are primary results
The Essence of Impact as Wave Propagation
Impact in solids propagates as an elastic longitudinal wave (P-wave) at the speed of sound c₀=√(E/ρ). For steel, c₀≈5000 m/s, meaning a stress wave takes only 20 μs to traverse a 100 mm component. The one-dimensional wave propagation theory organized by Kolsky in the 1950s remains the analytical foundation for Hopkinson bar tests today, serving as an essential method for evaluating material properties at strain rates of 10³–10⁴/s.
Computational Methods for Impact Analysis (Drop and Collision)
Impact Analysis Settings
Please tell me the specific FEM settings for impact analysis.
LS-DYNA
```
*KEYWORD
*CONTROL_TERMINATION
0.010 $ 10 ms
*CONTROL_TIMESTEP
0.0, 0.9 $ dt safety factor 0.9
*INITIAL_VELOCITY_SET
1, 0., 0., -5000. $ 5 m/s downward (in mm/s units)
*CONTACT_AUTOMATIC_SURFACE_TO_SURFACE
1, 2
```
Abaqus/Explicit
```
*STEP, NAME=impact
*DYNAMIC, EXPLICIT
, 0.010 $ 10 ms
*INITIAL CONDITIONS, TYPE=VELOCITY
impactor, 1, 0.
impactor, 2, 0.
impactor, 3, -5.0 $ 5 m/s
*CONTACT
...
*END STEP
```
So you set the initial velocity, and then the solver tracks the contact and deformation.
The explicit method is a "set the situation and let physics play out" approach. The user only defines initial conditions (velocity, position) and contact. The results emerge automatically according to physical laws.
Mesh Size Guideline
Mesh size for impact analysis:
| Target | Element Size |
|---|---|
| Contact Surface (Impact Area) | 1–5 mm |
| Remote Areas | 5–20 mm |
| Impactor (Rigid Body) | Coarse is OK |
Fine at the contact surface, coarse in remote areas.
Contact resolution directly affects the results. The area around the impact point needs 1–2 mm elements. However, finer meshes lead to smaller $\Delta t$, so balance with computational cost.
Summary
Designs Ignoring Strain Rate Dependence Are Dangerous
The yield stress of steel materials increases by 1.3–2 times at a strain rate of 10³/s compared to quasi-static (10⁻³/s) (Cowper-Symonds law). In LS-DYNA's MAT_003, velocity dependence is expressed by D·n parameters, with D=40.4, n=5.0 being widely used standard values for mild steel. Multiple studies report experimental data showing that ignoring this velocity effect in automotive bumper crash analysis leads to 20–40% overestimation of deformation.
Impact Analysis (Drop and Collision) in Practice
Impact Analysis in Practice
Main applications of impact analysis:
Related Topics
| Application | Standard | Condition |
|---|---|---|
| Smartphone Drop | Internal Company Standard | 1.5 m drop, concrete surface |
| Electronic Equipment Drop |