Cyclic response of 3D printed metamaterials with soft cellular architecture: The interplay between as-built defects, material and geometric non-linearity

The paper investigates the cyclic response of soft cellular materials undergoing repeated local instabilities. Our focus is mainly on the coupling between material non-linearities, geometric non-linearity as well as defects induced by 3D printing. Two paradigmatic lattices (triangular and hexagonal), each with its own distinct deformation mode and defect sensitivity, are examined, and the emergence of as-built material and geometric defects in the form of microporosity, strut thickness reduction, and nodal dispersion is studied via computed tomography and optical analyses. Experiments are carried out on the base material and lattice specimens for given cycling strains and cycle ratios. Numerical models are developed to understand the individual role of the main constitutive aspects of the base material, e.g. damage, creep, and visco-elasticity, as well as to assess the role of defects in each architecture. The results show that the activation of local buckling combined with the engagement of material non-linearities has multiple outcomes. It leads to local storage of inelastic strain, which in turn perturbs the lattice geometry after the second cycle and severely impacts the subsequent response, e.g. softening; it reduces the tangent modulus at zero strain; and it also decreases the maximum and minimum cyclic stresses. The detriment is further fueled by geometric deviations caused by 3D printing. Furthermore, a theoretical model is presented to obtain stress bound estimates of the stabilized response, hence offering guidelines for the design of 3D printed soft metamaterials under cycling loading. The paper concludes with a systematic discussion on the coupled role of non-linearities (material and geometry) and defects, and on the accuracy of the numerical and theoretical models herein presented.