A computational model for short-range van der Waals interactions between beams and shells

2026-02-27

AI Summary

This work addresses the challenge of efficiently and accurately modeling short-range van der Waals interactions—encompassing both attraction and repulsion—between beams and shells. A dimensionality-reduction integration strategy is proposed, decomposing the six-dimensional volume integral into a five-dimensional analytically pre-integrated component and a one-dimensional numerical integral. By coupling the Euler–Bernoulli beam and Kirchhoff–Love shell models, the total potential energy is discretized using isogeometric finite elements, and the resulting nonlinear equilibrium equations are solved via a continuation method. The approach achieves high accuracy at small separations while significantly enhancing computational efficiency. To the authors’ knowledge, this is the first systematic framework enabling reliable simulation of van der Waals interactions between beams and shells, with benchmark examples demonstrating excellent convergence and robustness.

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Abstract

We consider potential-based interactions between beams (or fibers) and shells (or membranes) using a coarse-grained approach with focus on van der Waals attraction and steric repulsion. The involved 6D integral over volumes of a beam and a shell is split into a 5D analytical pre-integration over the beam's cross section and a surrogate plate tangential to the closest point on the shell, and the remaining 1D numerical integration along the beam's axis. This general inverse-power interaction potential is added to the potential energies of the Bernoulli-Euler beam and the Kirchhoff-Love shell. The total potential energy is spatially discretized using isogeometric finite elements, and the nonlinear weak form of quasi-static equilibrium is solved using the continuation method. We provide error estimates and convergence analysis, together with two intriguing numerical examples. The developed approach provides excellent balance between accuracy and efficiency for small separations.

Problem

• van der Waals interactions
• beam-shell interaction
• short-range forces
• computational modeling
• coarse-grained approach

Innovation

• van der Waals interactions
• dimensional reduction
• isogeometric analysis
• beam-shell interaction
• continuation method