  The elastic response of dense suspensions under an impact is studied using
coupled Lattice Boltzmann Method and Discrete Element Method (LBM-DEM) and its
reduced model. We succeed to extract the elastic force acting on the impactor
in dense suspensions, which can exist even in the absence of percolating
clusters of suspended particles. We then propose a reduced model to describe
the motion of the impactor and demonstrate its relevancy through the comparison
of the solution of the reduced model and that of LBM-DEM. Furthermore, we
illustrate that the perturbation analysis of the reduced model captures the
short-time behavior of the impactor motion quantitatively. We apply this
reduced model to the impact of the foot-spring-body system on a dense
suspension, 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, the
foot undergoes multiple bounces. We also study the parameter dependencies of
the hopping motion and find that multiple bounces are suppressed as the spring
stiffness increases.
