# 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

## TL;DR

This paper introduces a novel 3D beam-to-beam interaction model for curved slender fibers undergoing large deformations, focusing on electrostatic, van der Waals, and steric forces, with a reduced computational approach for efficiency.

## Contribution

It presents the first 3D interaction model combining beam theory with a reduced section-to-section interaction law for efficient simulation of molecular forces between fibers.

## Key findings

- The SSIP approach significantly improves computational efficiency.
- Analytical expressions for short-range and long-range interactions are derived.
- Numerical examples validate the accuracy and robustness of the model.

## Abstract

This contribution proposes the first 3D beam-to-beam interaction model for molecular interactions between curved slender fibers undergoing large deformations. While the general model is not restricted to a specific beam formulation, in the present work it is combined with the geometrically exact beam theory and discretized via the finite element method. A direct evaluation of the total interaction potential for general 3D bodies requires the integration of contributions from molecule or charge distributions over the volumes of the interaction partners, leading to a 6D integral (two nested 3D integrals) that has to be solved numerically. Here, we propose a novel strategy to formulate reduced section-to-section interaction laws for the resultant interaction potential between a pair of cross-sections of two slender fibers such that only two 1D integrals along the fibers' length directions have to be solved numerically. This section-to-section interaction potential (SSIP) approach yields a significant gain in efficiency, which is essential to enable the simulation of relevant time and length scales for many practical applications. In a first step, the generic structure of SSIP laws, which is suitable for the most general interaction scenario (e.g. fibers with arbitrary cross-section shape and inhomogeneous atomic/charge density within the cross-section) is presented. Assuming circular, homogeneous cross-sections, in a next step, specific analytical expressions for SSIP laws describing short-range volume interactions (e.g. van der Waals or steric interactions) and long-range surface interactions (e.g. Coulomb interactions) are proposed. The validity of the SSIP laws as well as the accuracy and robustness of the general SSIP approach to beam-to-beam interactions is thoroughly verified by means of a set of numerical examples considering steric repulsion, electrostatic or van der Waals adhesion.