Experimental investigation and modeling of the temperature memory effect in a 4D-printed auxetic structure

4D printing is an innovative manufacturing approach that combines 3D printing and stimuli- responsive abilities to produce objects with complex geometry and capable of shapeshifting over time (the fourth dimension). To pursue such an approach this paper proposes to develop re-entrant honeycomb auxetic grids with tunable shape reconfigurable behavior. Particularly, the work combines 3D printing and a photopolymer exhibiting the so-called temperature memory effect (TME), a peculiar shape memory behavior expressing the capability of the material to remember not only the original shape but also the deformation temperature. A thorough experimental activity was carried out on single auxetic unit cells, chosen as representative of the whole auxetic grid, to properly highlight and assess their response upon heating after single-step and multiple-step deformation histories and to describe the recovery process as a function of time and temperature. Results demonstrate the possibility to achieve an easily controlled TME and to successfully exploit it for autonomous, complex hierarchical transformations over a large range of temperatures. As a proof-of-concept, the study of the sequential recovery of an entire auxetic grid subjected to double-step programming allowed highlighting a decoupled in-plane elongation and out-of-plane bending. The behavior of the 4D-printed auxetic structures was simulated by means of finite element (FE) analysis, using a thermoviscoelastic model of the photopolymer and viscoelastic experimental data obtained by time-temperature superposition analysis applied to multifrequency dynamic mechanical tests and to isothermal recovery tests. A good correspondence between experiments and simulations was obtained for all shape memory tests, demonstrating that the proposed FE approach is a suitable tool to support the design of these structures. The combination of 3D printing and TME opens new perspectives to achieve dynamic tunability in mechanical metamaterials, that is a key ingredient in several application fields