On the solitary wave dynamics of tensegrity lattices with stiffening response: a numerical study

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 triangu-lar tensegrity prisms with stiffening behavior support the propagation of compressive solitarywaves. We show that such result can be generalized to two-dimensional and three-dimensionalmodular tensegrity lattices composed of polygonal and polyhedral units. Differently from theone-dimensional case, the stiffening response of these lattices originates at the interface be-tween adjacent units, not from the unit themselves. We present numerical results on the responseto impulsive loads of slender assemblies composed by square units in two-dimensions, and cu-bic units in three-dimensions. We observed compact compressive waves forming at impactlocations, together with localized thermalization effects. Such compact waves propagate withnearly constant speed and energy, while maintaining their shape, and emerge from collisionwith other compact waves almost unaltered, losing a small fraction of their energy. These re-sults suggest the investigation of the dynamics of regular and quasi-regular tessellations formedby other types of polygonal and polyhedral units.