The present study investigates the behavior of solid cellular structures in polylactic acid (PLA), created using FDM technology (Fusion Deposition Modelling). The geometries are permanently deformed by compressive stress and then subjected to the recovery of the shape, through the application of a thermal stimulus. The structures are analyzed for medium-high and medium-low compression stresses, evaluating the mechanical properties and the absorption energy as the number of cycles varies. The study shows that the ability to absorb energy is related to the density of the model, as well as the degree of damage suffered, which increases with increasing number of load cycles. The strongest geometry is the Lozenge grid, which is the most reliable, because it shows no damage with increasing compression cycles and keeps its absorption rate almost constant. The increase in Lozenge grid density leads to an improvement in both mechanical strength and absorption energy, as well as a lower incidence of microcracks in the geometry itself due to the repeated load cycles.