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 noslip 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.

Magnetostriction in magnetic gels and elastomers as a function of the internal structure and particle distribution

“…In this case, the boundary can be approximated as a flat rigid wall. Our numerical results in this limit agree well with those of the Green's function calculated for a half-space filling elastic material bordered by a rigid no-slip boundary [73,74]. A similar solution exists for a half-space in the case of µ = 0 andμ → 0 with ν → 1/2, i.e.…”

Frequency-dependent magnetic susceptibility of magnetic nanoparticles in a polymer solution: a simulation study

“…Computational models exist on different scales of modelling. While continuum de- scriptions are well-suited to model MNP-polymer composites on a macro-level, [39][40][41][42][43] they typically lack details on the length scale of single polymers. This, however, will be necessary to study how individual changes to the polymer matrix affect its coupling to the embedded MNPs.…”

Tunable dynamic moduli of magnetic elastomers: from characterization by x-ray micro-computed tomography to mesoscopic modeling

“…Other approaches coarse-grain the polymer into a coupled mesh of nearly-incompressible tetrahedra [42,43], or, conversely, zoom onto the microscopic detail by resolving the individual polymer chains in a coarse-grained way [62,63]. Within the framework of linear elasticity theory, the matrix-mediated interactions between the particles can be calculated analytically and up to a desired order exactly [64][65][66][67][68].…”