Title: Force-induced elastic matrix-mediated interactions in the presence of a rigid wall,
Abstract: We consider an elastic composite material containing particulate inclusions
in a soft elastic matrix that is bounded by a rigid wall, e.g., the substrate.
If such a composite serves as a soft actuator, forces are imposed on or induced
between the embedded particles. We investigate how the presence of the rigid
wall affects the interactions between the inclusions in the elastic matrix. For
no-slip boundary conditions, we transfer Blake's derivation of a corresponding
Green's function from low-Reynolds-number hydrodynamics to the linearly elastic
case. Results for no-slip and free-slip surface conditions are compared to each
other and to the bulk behavior. Our results suggest that walls with free-slip
surface conditions are preferred when they serve as substrates for soft
actuators made from elastic composite materials. As we further demonstrate, the
presence of a rigid wall can qualitatively change the interactions between the
inclusions. In effect, it can switch attractive interactions into repulsive
ones (and vice versa). It should be straightforward to observe the effects in
future experiments and to combine our results, e.g., with the modeling of
biological cells and tissue on rigid surfaces.