Investigation of the peeling and pull-off behavior of adhesive elastic fibers via a novel computational beam interaction model

Abstract

This article studies the fundamental problem of separating two adhesive elastic fibers based on numerical simulation employing a recently developed finite element model for molecular interactions between curved slender fibers. Specifically, it covers the two-sided peeling and pull-off process starting from fibers contacting along its entire length to fully separated fibers including all intermediate configurations and the well-known physical instability of snapping into contact and snapping free. We analyze the resulting force-displacement curve showing a rich and highly nonlinear system behavior arising from the interplay of adhesion, mechanical contact interaction and structural resistance against (axial, shear and bending) deformation. While similar to one-sided peeling studies from the literature, a distinct initiation and peeling phase can be observed, the two-sided peeling setup considered in the present work reveals the extended final pull-off stage as third characteristic phase. Moreover, the influence of different material and interaction parameters such as Young's modulus as well as type (electrostatic or van der Waals) and strength of adhesion is critically studied. Most importantly, it is found that the maximum force occurs in the pull-off phase for electrostatic attraction, but in the initiation phase for van der Waals adhesion. In addition to the physical system behavior, the most important numerical aspects required to simulate this challenging computational problem in a robust and accurate manner are discussed. Thus, besides the insights gained into the considered two-fiber system, this study provides a proof of concept facilitating the application of the employed model to larger and increasingly complex systems of slender fibers.

A computational model for molecular interactions between curved slender fibers undergoing large 3D deformations with a focus on electrostatic, van der Waals, and repulsive steric forces

“…The numerical experiment of adhesive fibers studied in Reference reveals that this regularization yields the already mentioned great enhancement in terms of robustness as well as efficiency without any change in the system response. As shown in the comparison of the force‐displacement curves therein, the results obtained with the full LJ and with the regularized LJ force law do, indeed, coincide down to machine precision.…”

“…A remedy of this limitation could be a calibration, that is, a scaling of the prefactor k in the simple SSIP law, to fit a given reference solution within a small range of separations (eg, around the equilibrium distance of the LJ potential). In the authors' recent contribution, this pragmatic procedure is shown to reproduce the global system response very well. Still, it would be valuable to include the relative rotations of the cross‐sections in the applied SSIP law to obtain the correct asymptotic scaling behavior.…”

“…The results and conclusions discussed throughout this section are mainly based on the extensive numerical peeling and pull‐off experiment with two adhesive fibers, which is presented in the authors' recent contribution . In the absence of a regularization, only the pragmatic yet effective approach of applying a very restrictive upper bound of the displacement increment per nonlinear iteration (see Appendix C for details) proved successful to solve for the quasi‐static equilibrium configurations without occurrence of any invalid configuration g ≤0 for any integration point pair in any nonlinear iteration.…”

“…However, since during the nonlinear iterations also nonequilibrium configurations with g < g reg,LJ occur, the nonlinear solution procedure is influenced in an extremely positive way, leading to an overall saving of a factor of five in the number of nonlinear iterations as compared to the full LJ interaction without any regularization. For more details on the comparison, including all parameter values, we kindly refer the reader to Reference .…”

“…As a reference value for the applications we have in mind, the fiber radius R varies from several nanometers for DNA to millimeters for synthetic polymer fibers, resulting in a potentially very small normalized separation g / R . An example for the simulation of adhesive fibers in contact can be found in the authors' recent contribution, which studies the peeling and pull‐off behavior of two fibers attracting each other either via vdW or electrostatic forces.…”