A Computational Model for Molecular Interactions Between Curved Slender Fibers Undergoing Large 3D Deformations With a Focus on Electrostatic, van der Waals and Repulsive Steri

07/30/2019
by   Maximilian J. Grill, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/05/2022

Analytical disk-cylinder interaction potential laws for the computational modeling of adhesive, deformable (nano)fibers

The analysis of complex fibrous systems or materials on the micro- and n...
research
04/01/2022

Computation of optimal beams in weak turbulence

When an optical beam propagates through a turbulent medium such as the a...
research
10/27/2020

An isogeometric finite element formulation for geometrically exact Timoshenko beams with extensible directors

An isogeometric finite element formulation for geometrically and materia...
research
07/19/2019

A fibre Smart Displacement Based (FSDB) beam element for the nonlinear analysis of R/C members

Beam finite elements for non linear plastic analysis of beam-like struct...
research
09/21/2021

Geometrically exact static isogeometric analysis of an arbitrarily curved spatial Bernoulli-Euler beam

The objective of this research is the development of a geometrically exa...
research
11/14/2021

Visual design intuition: Predicting dynamic properties of beams from raw cross-section images

In this work we aim to mimic the human ability to acquire the intuition ...

Please sign up or login with your details

Forgot password? Click here to reset