Metamaterials are engineered materials designed to manifest distinct and exceptional properties at the macroscopic level. Presently, they represent a prominent and compelling subject of inquiry within the realm of material science. This work aims to create computational tools tailored for the design of a particular category of metamaterials: shock-absorbing dissipative metamaterials, aiming at two goals. The fast (macroscopic) shape recovery after impact from an external impactor and the subsequent loading release. Standard hyper-elastic materials fulfil the non-dissipation paradigm, but, if this paradigm is broken, they may exhibit relevant mechanical dissipation as the free energy turns non-convex. This work focuses on these cases at the macroscopic scale, yielding shock-absorbing metamaterials exhibiting dissipative behaviour at the upper scale, but made of polyconvex hyper-elastic materials at the low scale. The coupling between both scales is, then, responsible for the exotic dissipative behaviour at the macroscale. In this work, a microscale made of a buckling lattice of periodic cells is conceived as a mechanism to achieve the non-convexity of the free energy at the macro-scale, where some of their elastic members exhibit an appropriated buckling behaviour. The structural behaviour of the slender buckling members in the lattice (typically beams) is described in terms of degenerated kinematics, and, in turn, the upper scale is naturally described using standard 2D/3D solid formulations. The problem of translating the standard multi-scale formulations, established for settings in which the macro-scale and the micro-scale domains are described in a unique dimension space, into the intended unmatched dimensions case is solved by introducing an Ersatz material into the formulation. The lattice is designed as a sequence of sufficiently dimension-perturbed buckling layers so that instabilities arisen when the RVE is constituted by a number of a homogeneous set of layers is precluded. REFERENCES [1] Correa, Dixon M., et al. "Negative stiffness honeycombs for recoverable shock isolation." R. Protot. J. 21.2 (2015) [2] Nuñez-Labielle, A., et al. "Towards shock absorbing hyperelastic metamaterial design.(I) Macroscopic scale: Computational shock-capturing." CMAME (2022) [2] Saeb, Saba, Paul Steinmann, and Ali Javili. "Aspects of computational homogenization at finite deformations: a unifying review from Reuss' to Voigt's bound." A. Mech. Reviews (2016).