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Many practically relevant materials combine properties of viscous fluids andelastic solids to viscoelastic behavior. Our focus is on the induced dynamicbehavior of damped finite-sized particulate inclusions in such substances. Weexplicitly describe history-dependent interactions that emerge between theembedded particles. These interactions are mediated by the viscoelasticsurroundings. They result from the flows and distortions of the viscoelasticmedium when induced by the rigid inclusions. Both, viscoelastic environments ofterminal fluid-like flow or of completely reversible damped elastic behavior,are covered. For illustration and to highlight the role of the formalism inpotential applications, we briefly address the relevant examples of dragging arigid sphere through a viscoelastic environment together with subsequentrelaxation dynamics, the switching dynamics of magnetic fillers in elastic gelmatrices, and the swimming behavior of active microswimmers in viscoelasticsolutions. The approach provides a basis for more quantitative and extendedinvestigations of these and related systems in the future.

Memory-based mediated interactions between rigid particulate inclusions in viscoelastic environments