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The elastic response of dense suspensions under an impact is studied usingcoupled Lattice Boltzmann Method and Discrete Element Method (LBM-DEM) and itsreduced model. We succeed to extract the elastic force acting on the impactorin dense suspensions, which can exist even in the absence of percolatingclusters of suspended particles. We then propose a reduced model to describethe motion of the impactor and demonstrate its relevancy through the comparisonof the solution of the reduced model and that of LBM-DEM. Furthermore, weillustrate that the perturbation analysis of the reduced model captures theshort-time behavior of the impactor motion quantitatively. We apply thisreduced model to the impact of the foot-spring-body system on a densesuspension, which is the minimal model to realize walking on the suspension.Due to the spring force of the system and the stiffness of the suspension, thefoot undergoes multiple bounces. We also study the parameter dependencies ofthe hopping motion and find that multiple bounces are suppressed as the springstiffness increases.

Effective viscosity and elasticity in dense suspensions under impact: Toward a modeling of walking on suspensions