3D cubic auxetic structure with internal resonators: (a) cubic unit cell topology, (b) section view of the unit cell, (c) periodic lattice structure. (d) Schematic diagram of the simplified spring-mass model of the cubic re-entrant unit cell with external mass m₁, internal resonators mass m₂, external axial stiffness k₁ and internal axial stiffness k₂. (e) Schematic diagram of the periodic lattice with a number of unit cells.