Buckling is a critical failure mode in slender columns and rods under axial compression, significantly limiting their load-carrying capacity. Traditional optimization focuses on geometrical shapes, such as drum-shaped rods, or hollow structures to improve resistance. However, natural structures like plant stems and roots often exhibit superior buckling resistance due to their complex porous internal structures. This research aims to leverage biomimicry and machine learning to design artificial rods that surpass the buckling resistance of their natural inspirations. The study draws inspiration from various biological structures exhibiting excellent buckling characteristics, including plant stems (sedge, bulrush, clematis, bamboo, cactus, she-oak, mint), roots, animal quills, and seashells. These structures are characterized by diverse external shapes and intricate internal porous microstructures. By combining FEA modeling and machine learning, the researchers seek to identify design features that maximize buckling resistance, aiming to create artificial structures that outperform their biological counterparts. The significance lies in the potential for designing lighter, stronger, and more efficient engineering components for applications in various fields such as bridge and building construction.

Numerous studies have explored biomimicry for technological advancements. Examples include the self-cleaning properties of lotus leaves, inspiring self-cleaning surfaces; the fluid transportation mechanisms in plants, informing microfluidic devices; and the hook structures of plant burrs, leading to the invention of Velcro. Furthermore, the porous structures of pummelo fruit have been studied for their excellent damping properties, influencing the design of metallic foams. The research also notes prior work on using FEA to analyze buckling in columns and the enhanced buckling resistance of porous or hollow structures compared to solid ones. However, this work uniquely integrates FEA, 3D printing, and machine learning to systematically explore and optimize biomimetic designs for superior buckling properties.

The research involved several key steps: 1. **Selection of Biological Counterparts and Creation of Biomimetic Rods:** The researchers selected diverse plant stems and roots, idealizing their external shapes and internal porous structures. They created 21 basic biomimetic rod designs and then generated 1500 variations through modifications of pore shapes, sizes, and distributions. Solid and hollow cylindrical rods served as control groups. 2. **Buckling Load Analysis of Biomimetic Rods:** FEA using ANSYS was employed to determine the buckling load, stress, and displacement for each of the 1500 biomimetic rods. The mechanical properties of the 3D-printable Polylactic Acid (PLA) used were experimentally determined using a Q-TEST 150 machine, adhering to ASTM standard D695-15. Convergence analysis determined optimal FEA parameters. 3. **Experimental Validation:** Several representative biomimetic rods were 3D printed using a Creality CR-10S printer and subjected to uniaxial compression testing using the Q-TEST 150 machine to validate the FEA results. Buckling loads were recorded and compared with FEA predictions. 4. **Feature Identification or Fingerprints:** Each biomimetic rod was assigned a unique 'fingerprint' — a vector representing its geometrical features (e.g., outer shape, inner structure, pore locations, and sizes). This numerical representation was crucial for machine learning. 5. **Forward Design and Prediction:** Supervised machine learning was performed using MATLAB. 90% of the data were used for training a regression model to predict buckling load from the fingerprint data, and 10% was used for testing. The Ensemble Bagged Tree algorithm was found to provide the best prediction accuracy compared to SVM, GPR, and neural networks. 6. **Optimization:** A MATLAB code was developed to generate a vast number of potential fingerprint combinations. Data filtering in MATLAB and Excel then selected 160 designs with superior buckling strengths, which were then modeled and analyzed in ANSYS.

The results showed that biomimetic rods consistently exhibited significantly higher buckling capacity than solid and hollow rods of the same mass. Specifically, the normalized buckling capacity of biomimetic rods was more than twice that of the control rods. Stress analysis confirmed that failure occurred via buckling, not material failure. The experimental validation of FEA showed good agreement between simulation and experimental results. Machine learning accurately predicted buckling loads, and data filtering led to the identification of 160 optimized biomimetic rods. Critically, these optimized designs demonstrated nearly double the buckling strength of the initial biomimetic rods in the training dataset (1500 total designs). The optimized designs showed that combining specific external shapes (e.g., cactus and square) with continuous porous internal structures (like bamboo stems) produced the highest buckling resistance. Discontinuous porous structures (such as those mimicking quills or seashells) were found to be inferior.

The findings demonstrate the significant potential of combining biomimicry, FEA, and machine learning for the design of high-performance engineering structures. The optimized biomimetic rods show substantially improved buckling resistance compared to conventional designs without compromising significantly on weight or material stress. This approach offers a powerful tool for exploring a vast design space efficiently, potentially leading to lighter and stronger structures in various engineering applications. The success of the Ensemble Bagged Tree algorithm highlights the potential of machine learning for efficiently predicting material behavior and optimizing designs.

This research successfully demonstrated the creation and optimization of biomimetic rods with superior buckling resistance through a combined approach of biomimicry, FEA, and machine learning. The optimized designs show a significant improvement in buckling strength compared to traditional solid and hollow rods, opening up new possibilities for designing lightweight and highly resistant engineering structures. Future research could explore more complex biomimetic structures, investigate different materials, and expand the range of applications of this approach.

The study used a specific 3D printing method and material (PLA). The findings may not be directly generalizable to other materials or manufacturing techniques. The accuracy of the machine learning model depends on the quality and representativeness of the training data. Exploring a larger dataset with more diverse biomimetic designs could further improve the robustness and generalizability of the results. The printing resolution might have introduced minor discrepancies between simulation and experimental results.