🔬 applied physics

Dual-purpose architected materials: Optimizing graded BCC lattices for crashworthiness and heat dissipation

This paper proposes a multi-objective optimization framework for density-graded Body-Centered Cubic (BCC) lattices that simultaneously maximizes crashworthiness and heat dissipation, identifying optimal designs that effectively balance mechanical energy absorption with thermal performance through strategic density gradation.

Original authors: Jaswanth V Gurudev, Ratna Kumar Annabattula

Published 2026-02-20

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CC BY 4.0

Original authors: Jaswanth V Gurudev, Ratna Kumar Annabattula

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are designing a superhero shield for a car's electronic brain (like the computer that runs the engine or the battery). This shield has two very different jobs to do at the same time:

The Bodyguard Job: If the car crashes, the shield must crush itself to absorb the impact energy, protecting the delicate electronics inside. It needs to be squishy and strong.
The Air Conditioner Job: While the car is driving, the electronics get hot. The shield must let air flow through it easily to cool the chips down, acting like a high-tech radiator.

The Problem:
Usually, materials are good at one thing but bad at the other.

If you make the shield too thick and solid to stop a crash, air can't get through to cool it down (it gets hot).
If you make it full of holes to let air flow, it crumbles too easily in a crash (it doesn't protect).

The Solution: The "Graded" Lattice
The researchers in this paper came up with a clever idea using 3D printing. Instead of making the shield out of a uniform block of metal, they built it like a honeycomb (a lattice) made of tiny struts.

But here is the twist: They didn't make all the struts the same size. They made a Functionally Graded structure. Think of it like a staircase or a pyramid:

The Top (The "Cool" Side): The struts are very thin and delicate. This lets air rush through easily, like a wide-open window, to cool the electronics.
The Bottom (The "Hot" Side): The struts get thicker and stronger as you go down. This acts like a sturdy foundation, ready to take a heavy hit if the car crashes.

How They Found the Perfect Design
There are millions of ways to build this staircase. You could make the top super thin and the bottom super thick, or just slightly different. Testing every single possibility with a computer would take years.

So, the researchers used a smart shortcut (called "Surrogate Modeling"):

The Taste Test: They built and tested only 16 different versions of this lattice on a computer.
The Crystal Ball: They used math to create a "crystal ball" (a model) that could predict how any other version would perform based on those 16 tests.
The Balancing Act: They asked the computer: "Find us the design that is the best at both cooling and crashing, without sacrificing too much of one for the other."

The Results: Two Different Champions
The computer found two "winners," but they had very different personalities:

Design O1 (The "Cooling Specialist"):
- Pros: It lets air flow incredibly well and has a very low "peak stress" (it doesn't hit you with a sudden, jarring shock).
- Cons: It's terrible at absorbing crash energy. It's like a paper fan; it cools great, but if you drop a brick on it, it shatters. Also, because the bottom is so thick, the air gets stuck and can't actually cool the chip effectively.
- Verdict: Not a good choice. It fails at its main job (protection).
Design O2 (The "All-Rounder"):
- Pros: This is the Goldilocks design. It absorbs twice as much crash energy as the old standard design. It still cools very well (almost as good as the best cooler). It also reduces the air resistance, meaning the fan doesn't have to work as hard.
- How it works: It collapses in a perfect, orderly sequence, like a stack of cards falling one by one, rather than all at once. This absorbs energy smoothly without shocking the passengers.
- Verdict: The Winner. It does both jobs almost perfectly.

The Big Takeaway
This paper proves that by simply varying the thickness of the metal struts inside a lattice (making them thin at the top and thick at the bottom), we can create materials that are smarter than anything found in nature.

Instead of choosing between a "crash shield" and a "radiator," we can now build a single piece of material that is a super-shield and a super-cooler at the same time. This is a huge step forward for making safer, more efficient electric cars and electronics.

1. Problem Statement

Lattice structures, particularly Body-Centered Cubic (BCC) lattices, are promising candidates for applications requiring simultaneous mechanical energy absorption (crashworthiness) and thermal management (heat dissipation). However, existing optimization approaches typically focus on single-domain objectives (e.g., maximizing impact energy or minimizing peak stress) while neglecting the multi-physics trade-offs inherent in real-world scenarios.

The specific challenge addressed is the design of Functionally Graded (FG) BCC lattices for automotive electronic enclosures (e.g., Electronic Storage Units). These components face two simultaneous demands:

Thermal: Efficient passive heat extraction from chips via forced convection.
Mechanical: Protection against impact/crashes by absorbing kinetic energy without transmitting excessive peak stress to the protected components.

The authors hypothesize that a uniform lattice is suboptimal. Instead, a lattice with thicker struts on the heat source side (to maximize conduction and surface area) and thinner struts on the air inlet side (to minimize flow resistance and peak impact stress) could optimize both functions.

2. Methodology

A. Design Parameterization

Geometry: A BCC lattice with a $6 \times 6 \times 6$ unit cell arrangement (cell size = 4 mm).
Grading Strategy: The lattice is divided into three planar zones, resulting in four distinct strut diameter values ( $d_0, d_1, d_2, d_3$ ) from the bottom (heat side) to the top (air/impact side).
Constraints:
- $d_0$ is fixed at 0.5 mm (manufacturing limit).
- The relative density is maintained constant at $\rho = 0.17$ (same as the uniform "ground" lattice) to ensure a fair comparison.
- This constraint allows $d_3$ to be calculated as a function of $d_1$ and $d_2$ , reducing the design space to two variables ( $d_1, d_2$ ).
Analytical Approximation: To avoid complex volume calculations for graded struts, the authors derived an analytical expression for Area Porosity based on a 2D cross-section projection to enforce the relative density constraint.

B. Simulation Framework

Two independent physics simulations were conducted for 16 sampled design points (generated via Latin Hypercube Sampling):

Thermal (CFD):
- Solver: Ansys Fluent 2025 R1.
- Setup: Forced convection with air (15 m/s) impinging on a copper heat source (constant heat flux).
- Metrics: Nusselt number ($Nu$), Pressure drop ( $\Delta P$ ), and an effective thermal performance factor ( $\beta = Nu / C_f^{1/3}$ ).
Mechanical (Impact):
- Solver: Abaqus/Explicit.
- Setup: Dynamic crushing at 15 m/s between rigid plates.
- Material: Al-6061-T6 (linear-elastic, perfectly plastic).
- Metrics: Specific Energy Absorption (SEA), Peak Stress ( $\sigma_p$ ), and Densification Strain ( $\epsilon_D$ ).

C. Optimization Approach

Surrogate Modeling: Due to the high cost of running full simulations for every possible design, Thin Plate Spline - Radial Basis Functions (TPS-RBF) were used to construct surrogate models for the four metrics ( $Nu, SEA, \Delta P, \sigma_p$ ) based on the 16 training points.
Multi-Objective Optimization: Goal Programming was employed to find the optimal design ( $d_1^*, d_2^*$ ). The algorithm minimizes the weighted sum of deviations from ideal goals (max $Nu$, max $SEA$, min $\Delta P$ , min $\sigma_p$ ).

3. Key Contributions

Multi-Physics Framework: Development of a unified optimization framework that simultaneously addresses thermal and mechanical performance, moving beyond single-objective lattice design.
Strategic Grading Hypothesis: Validation that a specific density gradient (thicker at the heat source, thinner at the impact side) can decouple conflicting requirements, offering a superior alternative to uniform lattices.
Analytical Density Constraint: Derivation of an approximate analytical expression for area porosity to efficiently constrain the design space without full 3D volume integration.
Identification of Pareto-Optimal Designs: Discovery of two distinct optimal designs representing different trade-off strategies.

4. Results

A. Surrogate Model Performance

The TPS-RBF surrogates achieved near-perfect accuracy ( $R^2 = 1.0$ ) for all metrics. The analysis revealed:

Pressure Drop ( $\Delta P$ ): Linearly related to strut diameters (Darcy-Weisbach behavior).
Nusselt Number ($Nu$): Highly sensitive to $d_2$ ; highest values occur with the smallest top diameters ( $d_1, d_2$ ) and largest bottom diameter ( $d_3$ ).
Peak Stress ( $\sigma_p$ ): Minimized by thinner struts at the impact end.
Specific Energy Absorption (SEA): Maximized by a combination of low $d_1$ and high $d_2$ .

B. Optimal Designs (O1 vs. O2)

Two Pareto-optimal designs were identified:

Design O1 (Thermal-Optimized):
- Characteristics: Extremely thin top struts ( $d_1 \approx 0.5$ mm) and very thick bottom struts ( $d_3 \approx 2.45$ mm).
- Performance: Highest $Nu$ (+8.3%) and lowest $\Delta P$ (-35%).
- Failure: Catastrophic drop in SEA (-88%) due to "compound lattice" behavior where the thin top section collapses instantly, and the thick bottom section acts as a rigid solid, failing to absorb energy progressively. Chip temperature was also higher due to flow stagnation.
Design O2 (Balanced/Impact-Optimized):
- Characteristics: Moderately thin top struts ( $d_1 \approx 0.54$ mm) and moderately thick bottom struts ( $d_3 \approx 1.33$ mm).
- Performance:
  - SEA: +115% improvement over the ground lattice.
  - Peak Stress: -36% reduction.
  - Thermal: $Nu$ comparable to the ground lattice, but $\Delta P$ reduced by 31%.
  - Chip Temp: Lower than O1, indicating better actual heat extraction despite slightly lower $Nu$.
- Mechanism: Exhibits progressive layer-by-layer collapse, allowing for sustained energy absorption and higher densification strain ( $\epsilon_D$ ).

C. Validation

Simulations of the O1 and O2 designs confirmed the surrogate predictions with low error margins (e.g., <5% for SEA and $\Delta P$ ), validating the optimization framework.

5. Significance and Conclusion

This study demonstrates that strategic density gradation in BCC lattices can effectively resolve the trade-off between crashworthiness and thermal management.

Key Insight: Simply maximizing surface area (thick struts everywhere) or minimizing flow resistance (thin struts everywhere) is insufficient. The optimal solution lies in a linear density gradient (Design O2) that facilitates progressive collapse for energy absorption while maintaining sufficient porosity for airflow.
Application: The O2 lattice is identified as the superior candidate for automotive electronic enclosures, offering a 115% increase in energy absorption and a 31% reduction in pumping power (pressure drop) compared to uniform lattices, without compromising thermal performance.
Future Work: The authors suggest extending this framework to other topologies (FCC, Diamond) and integrating Physics-Informed Geometric Operators (PIGOs) to reduce reliance on expensive simulations and discover higher-order latent variables governing lattice behavior.