TY - JOUR
T1 - Analytical disk–cylinder interaction potential laws for the computational modeling of adhesive, deformable (nano)fibers
AU - Grill, Maximilian J.
AU - Wall, Wolfgang A.
AU - Meier, Christoph
N1 - Publisher Copyright:
© 2023 Elsevier Ltd
PY - 2023/5/1
Y1 - 2023/5/1
N2 - The analysis of complex fibrous systems or materials on the micro- and nanoscale, which have a high practical relevance for many technical or biological systems, requires accurate analytical descriptions of the adhesive and repulsive forces acting on the fiber surfaces. While such analytical expressions are generally needed both for theoretical studies and for computer-based simulations, the latter motivates us here to derive disk–cylinder interaction potential laws that are valid for arbitrary mutual orientations in the decisive regime of small surface separations. The chosen type of fundamental point-pair interaction follows the simple Lennard-Jones model with inverse power laws for both the adhesive van der Waals part and the steric, repulsive part. We present three different solutions, ranging from highest accuracy to the best trade-off between simplicity of the expression and sufficient accuracy for our intended use. The validity of simplifying approximations and the accuracy of the derived potential laws is thoroughly analyzed, using both numerical and analytical reference solutions for specific interaction cases. Most importantly, the correct asymptotic scaling behavior in the decisive regime of small separations is achieved, and also the theoretically predicted (1/sinα)-angle dependence (for non-parallel cylinders) is obtained by the proposed analytical solutions. As we show in the outlook to our current research, the derived analytical disk–cylinder interaction potential laws may be used to formulate highly efficient computational models for the interaction of arbitrarily curved fibers, such that the disk represents the cross-section of the first and the cylinder a local approximation to the shape of the second fiber.
AB - The analysis of complex fibrous systems or materials on the micro- and nanoscale, which have a high practical relevance for many technical or biological systems, requires accurate analytical descriptions of the adhesive and repulsive forces acting on the fiber surfaces. While such analytical expressions are generally needed both for theoretical studies and for computer-based simulations, the latter motivates us here to derive disk–cylinder interaction potential laws that are valid for arbitrary mutual orientations in the decisive regime of small surface separations. The chosen type of fundamental point-pair interaction follows the simple Lennard-Jones model with inverse power laws for both the adhesive van der Waals part and the steric, repulsive part. We present three different solutions, ranging from highest accuracy to the best trade-off between simplicity of the expression and sufficient accuracy for our intended use. The validity of simplifying approximations and the accuracy of the derived potential laws is thoroughly analyzed, using both numerical and analytical reference solutions for specific interaction cases. Most importantly, the correct asymptotic scaling behavior in the decisive regime of small separations is achieved, and also the theoretically predicted (1/sinα)-angle dependence (for non-parallel cylinders) is obtained by the proposed analytical solutions. As we show in the outlook to our current research, the derived analytical disk–cylinder interaction potential laws may be used to formulate highly efficient computational models for the interaction of arbitrarily curved fibers, such that the disk represents the cross-section of the first and the cylinder a local approximation to the shape of the second fiber.
KW - Fibers
KW - Intermolecular forces
KW - Lennard–Jones potential
KW - Van der Waals interaction
UR - http://www.scopus.com/inward/record.url?scp=85149686025&partnerID=8YFLogxK
U2 - 10.1016/j.ijsolstr.2023.112175
DO - 10.1016/j.ijsolstr.2023.112175
M3 - Article
AN - SCOPUS:85149686025
SN - 0020-7683
VL - 269
JO - International Journal of Solids and Structures
JF - International Journal of Solids and Structures
M1 - 112175
ER -