We present some peculiar results about the solitary-wave dynamics of novel tensegrity-based metamaterials. It has been previously shown that one-dimensional chains of triangular tensegrity prisms with stiffening behavior support the propagation of compressive solitary waves. We show that such result can be generalized to two-dimensional and three-dimensional modular tensegrity lattices composed of polygonal and polyhedral units. Differently from the one-dimensional case, the stiffening response of these lattices originates at the interface between adjacent units, not from the unit themselves. We present numerical results on the response to impulsive loads of slender assemblies composed by square units in two-dimensions, and cubic units in three-dimensions. We observed compact compressive waves forming at impact locations, together with localized thermalization effects. Such compact waves propagate with nearly constant speed and energy, while maintaining their shape, and emerge from collision with other compact waves almost unaltered, losing a small fraction of their energy. These results suggest the investigation of the dynamics of regular and quasi-regular tessellations formed by other types of polygonal and polyhedral units.
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