Simulating deformable impacts

The Problem: Why Collisions Are More Than Just “Bouncing”

Inelastic collisions—where objects don’t just rebound but deform, stick, or fragment—are governed by nonlinear dynamics that defy simple equations. Traditional models often oversimplify contact mechanics, ignoring how materials adapt during impact. For instance, a soft robot’s silicone “fingers” gripping an object or a water droplet splashing on a vibrating surface involves intricate coupling between elasticity, fluid dynamics, and geometry .

The KM Framework: Smoothing Out the Chaos

At its core, the KM framework introduces (see (Agüero et al., 2022)) a geometric constraint on contacting surfaces: the angle of incidence between colliding objects must remain smooth. Think of it as ensuring a “handshake” between materials—no sharp edges, no sudden jumps. This approach is:

1. Intuitive: Unlike brute-force simulations, KM’s constraints mirror real-world behavior, making it easier to implement .
2. Versatile: It works with finite elements, finite differences, or even machine learning solvers.
3. Efficient: By avoiding costly mesh refinements, KM excels in scenarios like low-velocity droplet impacts, where traditional methods struggle .

In our recent work , we validated KM against experiments involving a rigid sphere striking an elastic membrane. The results matched not just deformation patterns but also energy dissipation rates—a rarity in collision modeling .

From Robots to Raindrops: Why This Matters

1. Soft Robotics

KM enables precise modeling of grippers interacting with delicate objects, ensuring forces are distributed without damage—critical for medical robotics or fruit-picking machines.

2. Astrophysics

Simulating asteroid collisions or planetary accretion requires handling fragmented, deformable bodies. KM’s ability to manage irregular contact surfaces could refine models of cosmic dust aggregation .

3. Fluid-Structure Interactions

Our most recent work ((Gabbard et al., 2025)) applies KM to water droplets hitting fluid baths—a problem with applications in inkjet printing and pesticide spraying. Early results show KM captures capillary waves and coalescence better than conventional CFD .

What’s Next?

We’re expanding KM to:

• Multi-material collisions: Think ice hitting water (relevant for cryogenic engineering).
• Biological systems: Simulating cell-matrix interactions in tissue engineering bioreactors .
• Machine learning integration: Training neural networks to predict KM constraints, reducing compute time.

Collisions aren’t just endpoints—they’re conversations between materials. With KM, we’re decoding that dialogue, one impact at a time. 🚀