Refining the Understanding of Tube Collapse Mechanics

For decades, the collapse behavior of thin-walled circular tubes has captivated structural engineers due to its critical role in crashworthiness, energy absorption, & structural stability in automotive, aerospace, & civil engineering. While the “ring mode” of deformation has long been theoretically modeled & validated, the “diamond mode” has remained an elusive phenomenon. A new study by Zhou, Rong, Liu, & Wu, published in Scientific Reports (2025), shines a spotlight on the axial crushing behavior of stainless-steel circular tubes in diamond mode, aiming to fill this theoretical vacuum.

Laboratory Validation: Experiments on Stainless Steel Tubes

The team conducted a series of controlled experiments involving three sets of 304 stainless-steel circular tubes. These tubes had varying diameter-to-thickness (D/t) ratios ranging from 50 to 200. The test results revealed that the diamond mode only initiates when D/t surpasses 50, validating prior assumptions. Under compressive loads, these tubes exhibited lobed wrinkles along their circumference, distinct indicators of diamond mode deformation. The experimental phase provided high-fidelity data to calibrate & verify the subsequent numerical simulations.

Simulating the Imperfection-Triggered Diamond Fold Patterns

The researchers used advanced finite element analysis to replicate and extend the experimental findings. Small geometric imperfections were artificially introduced to the numerical models to deliberately trigger diamond mode collapses. The simulations revealed that depending on the D/t ratio, the tubes developed 3 to 7 circumferential lobes. These lobes formed diamond-shaped folds, absorbing energy progressively during axial compression. The simulation data allowed the authors to derive a new empirical formula for the normalized mean crushing stroke, critical for safety engineering designs.

Geometric Modeling & Wrinkle Evolution Analysis

Using both experimental and numerical observations, the team constructed a geometric model to better understand the wrinkle formation and folding process. Notably, their analysis found that the lobes were not sharply angular as previously believed but had finite curvature along the circumferential direction. This led to a more accurate representation of energy dissipation through plastic deformation. The research also predicted the maximum number of circumferential lobes possible for a given D/t ratio, helping engineers design tubes that collapse efficiently rather than catastrophically.

A New Theoretical Model to Calculate Crushing Force

The cornerstone of the research lies in the formulation of a new theoretical model to estimate the mean crushing force of circular tubes undergoing diamond mode deformation. Unlike older models by Pugsley or Johnson, this new approach accounts for the real geometric profiles of folds, lobe count, and plastic hinge formations. The model demonstrates strong agreement with both simulated and experimental data, offering engineers a much-needed predictive tool. The authors propose that this framework be adopted for future design codes & crashworthiness assessments.

Addressing Prior Limitations in Diamond Mode Theories

Previous theoretical models often oversimplified the diamond fold shape or failed to predict crushing forces accurately when the number of lobes (N) exceeded 3 or 4. Abramowicz and Singace’s models, while pioneering, could not account for the variations in wrinkle width or complex hinge line distributions observed in real tests. This study surpasses those limitations by redefining the fold's structural geometry and proposing an energy-based model that aligns well across multiple D/t and lobe-number scenarios.

Implications for Energy-Absorbing Design Applications

The implications of this study are significant across multiple engineering domains. Thin-walled tubes are widely used in vehicle crumple zones, train buffers, aerospace structures, and offshore platforms. By enabling better predictions of collapse forces and folding behavior, this research can lead to safer, more efficient designs. The newly developed formulae and geometric models empower engineers to tailor materials and structures for optimized energy absorption during high-impact events.

Key Takeaways:

• The study experimentally & numerically investigates diamond mode collapse in stainless-steel tubes with D/t ratios from 50 to 200, revealing 3–7 circumferential lobes.

• A new theoretical model was proposed to estimate mean crushing force, offering high accuracy compared to earlier models.

• The geometric model redefines lobe shapes & wrinkle profiles, correcting prior oversimplifications in diamond mode theory.