Published now: New analytical laws and applications of interaction potentials with a focus on van der Waals attraction

Our latest publication, "New analytical laws and applications of interaction potentials with a focus on van der Waals attraction", is now available as part of the Applied Mathematical Modelling, Volume 145, September 2025, 116100 by Elsevier.

The authors are: A. Borković, M.H. Gfrerer, R.A. Sauer

Abstract:
The paper aims to improve the efficiency of modeling interactions between slender deformable bodies that resemble the shape of fibers. Interaction potentials are modeled as inverse-power laws with respect to the point-pair distance, and the complete body-body potential is obtained by pairwise summation (integration). To speed-up integration, we consider the analytical pre-integration of potentials between specific geometries such as disks, cylinders, rectangles, and rectangular prisms. Several exact new interaction laws are obtained, such as disk-infinite half-space and (in-plane) rectangle-rectangle for an arbitrary exponent, and disk-disk and rectangle-rectangle for van der Waals attraction. To balance efficiency and accuracy, approximate laws are proposed for disk-disk, point-cylinder, and disk-cylinder interactions. Additionally, we have developed a novel formulation for the interaction between a spatial beam and an infinite half-space. The application of the pre-integrated interaction potentials within the finite element method is illustrated via two examples.

The full text can be accessed here:

https://doi.org/10.1016/j.apm.2025.116100