Efficient snap-to-contact computations for van der Waals interacting fibers

TL;DR

This paper introduces an efficient computational method for modeling van der Waals interactions between fibers, combining analytical pre-integration and numerical methods to handle complex nonlinear and dynamic contact phenomena.

Contribution

It presents a novel approach that combines coarse-graining, analytical pre-integration, and isogeometric finite elements for efficient simulation of fiber interactions.

Findings

Pre-integration reduces computational cost significantly.

The method accurately captures nonlinear and dynamic snap-to-contact events.

Coarse-graining enables modeling at small length scales efficiently.

Abstract

We consider van der Waals interactions between in-plane fibers, where the computational model employs the Lennard-Jones potential and the coarse-grained approach. The involved 6D integral over two interacting fibers is split into a 4D analytical pre-integration over cross sections and the remaining 2D numerical integration along the fibers' axes. Two section-section interaction laws are implemented, refined, and compared. Fibers are modeled using the Bernoulli-Euler beam theory and spatially discretized with isogeometric finite elements. We derive and solve the weak form of both quasi-static and dynamic boundary value problems. Four numerical examples involving highly nonlinear and dynamic snap-to-contact phenomena are scrutinized. We observe that the coarse-graining and pre-integration of interaction potentials enable the efficient modeling of complex phenomena at small length scales.