AUTHOR=Filippov A. D. , Sharma P. , Helmendach F. , Dijksman J. A. , Hidalgo R. C. 

TITLE=Fibre bundle models as a framework for the detachment dynamics of soft probabilistic fasteners

JOURNAL=Frontiers in Physics

VOLUME=12

YEAR=2024

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2024.1412352

DOI=10.3389/fphy.2024.1412352

ISSN=2296-424X

ABSTRACT=<p>Adhesives can be made by patterning surfaces with discrete adhesive elements. Nature uses this approach to provide animals with highly adaptive and robust approaches towards gaining an effective grip on surfaces. The mechanism of patterned surface adhesion involve many different attachment principles, adhesive site interactions, and probabilistic effects, the interplay of which is not understood. This limits our ability to design patterned surface adhesives for engineering applications. In this work, we quantify how a mechanically patterned adhesive based on passive mushroom-shaped elements performs. We explore a range of surface design features and model the mechanical adhesion dynamics with an approach based on the fiber bundle model (FBM). We find that the fiber bundle model can be used to rationalize the observations after modifying it to capture the initial non-linear force response of the adhesives. Additionally, we investigate the behavior of the system’s elastic energy and damage energy, as it is stretched under strain-controlled conditions. Our experimental data indicates that the elastic energy has a maximum that appears after the macroscopic strength <inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mrow><mml:mtext>c</mml:mtext></mml:mrow></mml:msub></mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math></inline-formula>, corresponding to strains where a full rupture of the system can no longer be prevented. Moreover, we observed that below the maximum of the constitutive curve <inline-formula id="inf2"><mml:math id="m2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mrow><mml:mtext>c</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula>, the elastic energy consistently exceeds the damage energy. Finally, we found that the derivative of the elastic energy has a maximum, which always appears before <inline-formula id="inf3"><mml:math id="m3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>σ</mml:mi></mml:mrow><mml:mrow><mml:mtext>c</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula>. Therefore, the derivative of the elastic energy would serve as a reliable signal of upcoming catastrophic failure in experiments under stress-controlled conditions.</p>