# Forces on rigid inclusions in elastic media and resulting matrix-mediated interactions

## TL;DR

This paper derives analytical expressions for the elastic interactions between spherical particles embedded in elastic media, supported by experiments with magnetic particles, aiming to extend hydrodynamic interaction methods to elasticity.

## Contribution

It introduces a novel analytical approach to calculate elastic interactions between particles in elastic media, inspired by hydrodynamic interaction techniques.

## Key findings

- Analytical formulas for particle interactions in elastic media
- Experimental validation with magnetic particles
- Potential applications in elastic composite materials

## Abstract

To describe many-particle systems suspended in incompressible low-Reynolds-number fluids, effective hydrodynamic interactions can be introduced. Here, we consider particles embedded in elastic media. The effective elastic interactions between spherical particles are calculated analytically, inspired by the approach in the fluid case. Our experiments on interacting magnetic particles confirm the theory. In view of the huge success of the method in hydrodynamics, we similarly expect many future applications in the elastic case, e.g. for elastic composite materials.