E25 Biomimetic optimization

Topic

This biomimetic optimization seeks to extract the design principle from the natural adhesive mushroom—a model established elsewhere in this study—to create a specific, reusable artificial adhesive.

The "split-contact" theorem—a principle also established in this study—posits that the total adhesive force scales with the square root of the mushroom density, thereby incentivizing the maximization of contact points between the mushrooms and the surface.

Conversely, the Glassmaker criterion sets a limit on this maximization: a mushroom that is too thin or too long will collapse and stick to a neighboring mushroom—a phenomenon of agglomeration also modeled in this study—thereby losing its specific adhesive functionality.

The optimal mushroom configuration is determined by the balance between its elastic restoring force (which keeps it upright) and the lateral adhesive force (which pulls it toward a neighbor). If the elastic restoring force significantly exceeds the lateral adhesive force, the mushroom remains upright and more stable against the aforementioned collapse.

The objective function for this biomimetic design includes a penalty term for unwanted stiffness, thereby modeling the trade-off between adhesion and ease of detachment—another aspect modeled in this study. Consequently, this model—based on the design principle of a natural adhesive mushroom—utilizes an artificial adhesive structure where the optimal final tilt angle of the artificial mushroom maximizes the resulting tangential force, given the adhesive friction coefficient established elsewhere in the framework. As the tilt angle of the artificial mushroom approaches this specific optimum, the resulting tangential force increases further, thereby bringing the performance of the artificial adhesive closer to that of the natural adhesive mushroom itself.

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