A novel section-section potential for short-range interactions between plane beams

TL;DR

This paper introduces a new interaction potential law for in-plane beams that accounts for cross-section offsets, enhancing accuracy in modeling short-range intermolecular forces like van der Waals and steric interactions.

Contribution

A novel, asymptotically consistent formulation for section-section interaction potential that improves modeling of short-range forces between deformable fibers.

Findings

Enhanced accuracy in numerical simulations of fiber interactions.

Successful application to peeling and pull-off scenarios.

Framework compatible with isogeometric Bernoulli-Euler beams.

Abstract

We derive a novel formulation for the interaction potential between deformable fibers due to short-range fields arising from intermolecular forces. The formulation improves the existing section-section interaction potential law for in-plane beams by considering an offset between interacting cross sections. The new law is asymptotically consistent, which is particularly beneficial for computationally demanding scenarios involving short-range interactions like van der Waals and steric forces. The formulation is implemented within a framework of rotation-free Bernoulli-Euler beams utilizing the isogeometric paradigm. The improved accuracy of the novel law is confirmed through thorough numerical studies. We apply the developed formulation to investigate the complex behavior observed during peeling and pull-off of elastic fibers interacting via the Lennard-Jones potential.