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 a 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.

KEYWORDS:

• Adhesive fibers
• mechanical properties of adhesives
• peel
• numerical analysis
• nonlinear finite-element analysis
• geometrically exact beam theory
• van der Waals interaction
• electrostatic interaction

Notes

¹ The resulting peeling force values showed a noticeable unphysical dependence on both the type of the penalty force law and the value of the penalty parameter $\epsilon$.

² The steady state has been defined in a way that the magnitude of every velocity and acceleration component in the system has fallen below a threshold value of.

³ This shape will be even more pronounced for a smaller value of Young’s modulus, cf. Figure 5(b).

⁴ Since the penalty contact formulation is considered to be a numerical regularization of the non-penetration constraint rather than a physically motivated repulsive force law (refer to the discussion in Section 2.3), we suggest to keep this ratio $\epsilon /({\sigma }^2{k}_{\mathrm{e}\mathrm{l}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}}R)$ fixed when varying the adhesive strength, such that an increased adhesive strength does not lead to an increased violation of the non-penetration constraint.

⁵ Although using the precise sequence of amino acids of the mucin macromolecule would lead to a much more complex line charge distribution than the homogeneous charge density considered in this study, the corresponding line charge densities are known to lie in the range of $\lambda =2\pi R\sigma \in [1\mathrm{e}/1.2\mathrm{n}\mathrm{m},1\mathrm{e}/10\mathrm{n}\mathrm{m}]$. Bearing in mind the neglect of charge screening effects (as typically observed in electrolyte solutions under physiological conditions), the parameters of the current computational model should be interpreted as effective charge densities and the values for the real charge densities obtained from analysis of the sequence of amino acids would need to be decreased to account for this modeling assumption.