Here’s the ranked importance of the variables for predicting and maximizing **toughness** of 3-D printed crossed-barrel structures:

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## 📊 Variable Importance Ranking

1. **θ (theta, crossing angle)**

   * **Rationale:** Crossing angle directly governs load path redirection, stress distribution, and crack deflection. In lattice/fracture mechanics, angle has the strongest influence on whether cracks propagate straight or are arrested. Prior studies on architected lattices show that geometry (angle/orientation) dominates toughness.

2. **t (wall thickness)**

   * **Rationale:** Thickness controls ligament strength and plastic energy absorption. Increasing *t* improves fracture resistance up to a point, but overly thick walls reduce ductility (leading to brittle fracture). Strong secondary driver of toughness.

3. **r (normalized radius)**

   * **Rationale:** Radius affects curvature, contact area, and local stress concentration. Larger *r* generally spreads stress and delays crack initiation, but its effect is subtler than angle/thickness.

4. **n (number of unit cells)**

   * **Rationale:** More cells change overall specimen size and distribution of fracture events. However, toughness (energy absorbed per fracture event) usually scales more with *local geometry* (θ, t, r) than global count. Effects are indirect (boundary conditions, size effects).

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## ✅ Final Ranking

**θ > t > r > n**

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Would you like me to also suggest **interaction terms** (e.g., θ×t, r×t) that are likely to be important for Bayesian optimization, not just the main effects?
