On the presence of a critical detachment angle in gecko spatula peeling - a numerical investigation using an adhesive friction model

ABSTRACT

A continuum-based computational contact model is employed to study coupled adhesion and friction in gecko spatulae. Nonlinear finite element analysis is carried out to simulate spatula peeling from a rigid substrate. It is shown that the “frictional adhesion” behavior, until now only observed from seta to toe levels, is also present at the spatula level. It is shown that for sufficiently small spatula pad thickness, the spatula detaches at a constant angle known as the critical detachment angle irrespective of the peeling and shaft angles. The spatula reaches the same energy states at the jump-off contact point, which directly relates to the invariance of the critical detachment angle. This study also reveals that there is an optimum pad thickness associated with the invariance of the critical detachment angle. It is further observed that the sliding of the spatula pad is essential for the invariance of the critical detachment angle. Further, it is found that the invariance of the critical detachment angle is unaffected for a wide range of spatula shaft lengths.

KEYWORDS:

• Gecko adhesion
• nonlinear finite element analysis
• computational contact
• adhesive friction
• critical detachment angle

Acknowledgements

The authors are grateful to the SERB, DST for supporting this research under project SR/FTP/ETA-0008/2014. The authors thank Dr. David Labonte for his valuable comments.

Notes

¹ the present authors prefer the term “adhesive friction” instead of “frictional adhesion” in order to describe the interaction between friction and adhesion as friction depends on adhesion (and not vice versa) according to the coupled adhesion-friction model used here (see Equation (3)(3) $T_{\mathrm{s}\mathrm{l}}(d_{\mathrm{s}})=\left\{\begin{array}{cc}\frac{{\mu }_{\mathrm{s}}}{J_{\mathrm{c}\mathrm{l}}}[T_{\mathrm{a}}(d_{\mathrm{s}})-T_{\mathrm{a}}(d_{\mathrm{c}\mathrm{u}\mathrm{t}})],& d_{\mathrm{s}}<d_{\mathrm{c}\mathrm{u}\mathrm{t}},\\ 0,& d_{\mathrm{s}}\ge d_{\mathrm{c}\mathrm{u}\mathrm{t}},\end{array}\right.$(3) ).

² As the spatula is very wide (up to a few hundred nm), plane strain is a reasonable simplification of the full 3D case.

³ As the L-J potential is a continuously varying function, a cut-off criterion is assumed in the current study to define when spatula detachment starts. It is assumed that detachment has started, if at least one of the contact surface points is displaced such that the adhesive traction acting at that point becomes less than $95\mathrm{\%}$ of the maximum adhesive traction.

Additional information

Funding

This work was supported by the Science and Engineering Research Board [SR/FTP/ETA-0008/2014].