Optimizing the Energy Absorption Capacity of Auxetic Mechanical Metamaterials by Density Gradation

Mechanical metamaterials with rotating squares have attracted considerable attention due to their adjustable shape control, strength, and energy absorption characteristics. Prior research suggests that the load-bearing and energy absorption capacities of these structures can be tailored by varying the stiffness and/or thickness of the hinges that connect the solid portions of the unit cells (squares) in the structures. However, this strength-energy absorption dichotomy has hindered the design and implementation of these structures in practical applications. The objective of this study is to apply the ‘density gradation’ approach to designing novel rotating-square metamaterials with simultaneously enhanced strength and energy absorption capacities with minimized structural weight. Uniform density rotating-square metamaterials are designed and fabricated using SLA 3D printing with various cell hinge thicknesses. The global force-displacement curves of these uniform-density structures are obtained experimentally under quasi-static and impact loading conditions. This data is then used as the input to a predictive model that enables the virtual assessment of the constitutive response of density-graded structures with various gradient functions. The predictive model results are verified by full-field experimental measurements conducted on selected density-graded structures subjected to low and intermediate-velocity impact conditions. The role of variable cell hinge thickness is discussed in terms of the local mechanical constraints imposed by these components on the rotational degree of freedom of the solid squares in the structure, concurrently causing a nonlinear strain hardening behavior. The results discussed in this work provide a practical solution to the strength-energy absorption dichotomy in cellular structures, opening new doors to precise control of mechanical behavior in auxetic mechanical metamaterials for impact mitigation applications.