Elastic displacements and viscous hydrodynamic flows in wedge-shaped geometries with a straight edge: Green's functions for parallel forces
Abstract
For homogeneous and isotropic linearly elastic solids and for incompressible fluids under low-Reynolds-number conditions the fundamental solutions of the associated continuum equations were derived a long time ago for bulk systems. That is, the corresponding Green's functions are available in infinitely extended systems, where boundaries do not play any role. However, introducing boundaries renders the situation significantly more complex. Here, we derive the corresponding Green's functions for a linearly elastic homogeneous and isotropic material in a wedge-shaped geometry. Two flat boundaries confine the material and meet at a straight edge. No-slip and free-slip conditions are considered. The force is oriented in a direction parallel to the straight edge of the wedge. Assuming incompressibility, our expressions also apply to the situation of low-Reynolds-number hydrodynamic viscous fluid flows. Thus, they may be used, for instance, to describe the motion of self-propelled objects guided by an edge or the distortion of soft elastic actuators in wedge-shaped environments of operation.
Keywords
Cite
@article{arxiv.2503.16116,
title = {Elastic displacements and viscous hydrodynamic flows in wedge-shaped geometries with a straight edge: Green's functions for parallel forces},
author = {Abdallah Daddi-Moussa-Ider and Lukas Fischer and Marc Pradas and Andreas M. Menzel},
journal= {arXiv preprint arXiv:2503.16116},
year = {2026}
}
Comments
Accepted in Proc. R. Soc. A