Self-contact-induced stiffening in curved-ligament re-entrant lattice metamaterials

This work investigates the compressive response of curved-ligament re-entrant lattice metamaterials in which internal self-contact acts as a geometry-controlled stiffening mechanism. Under compression, neighbouring ligaments progressively come into contact within the central neck region, introducing additional constraints and modifying the load-transfer paths. Two complementary numerical analyses are performed. First, the effective elastic response of the undeformed periodic cell is characterized through first-order computational homogenization with periodic boundary conditions. This provides a reference description of the initial open-cell regime and of the elastic anisotropy before contact activation. Second, nonlinear compression simulations with frictionless self-contact are used to investigate the response beyond the initial open-cell regime. The results show that contact activation is directly associated with the departure from the initial compliant regime and with a progressive increase in the slope of the force–displacement response. Within the selected set of representative geometries, ligament spacing mainly affects the displacement range over which the cell remains open, whereas aspect ratio and ligament number influence the spatial distribution of the active contact regions. Overall, the results indicate that geometry-dependent self-contact can be exploited to tailor the nonlinear compressive response of curved-ligament lattice architectures. The observed stiffening originates from contact activation rather than from material nonlinearities or additional internal components.