Modeling and Design of Periodic Polygonal Lattices Constructed from Microstructures with Varying Curvatures

Lattice structures can exhibit unusual mechanical properties by appropriate design and arrangement of the microstructures, and have already found applications in areas such as tissue engineering, stretchable electronics, and soft robotics. However, the designed microstructures generally follow simple geometric patterns with constant curvatures and theoretical models are developed for each geometry particularly. It lacks a universal method to model and design the periodic lattice constructed from microstructures with varying curvatures. In this paper, we develop a universal approach to design polygonal lattices with a wide range of microstructures with varying curvatures using instant curvature and parametric functions. A finite deformation model is proposed for the microstructures and the corresponding lattices, which considers the wavy or curled microstructure, hierarchical geometry, and large deformation. Experiments and finite-element simulations are conducted to validate the theoretical model. All of Young's modulus, stretchability, and Poisson's ratio can be inversely designed using the developed theoretical model. Results show that the stretchability of the highly stretchable lattice can be further increased by more than 4 times using densely curled microstructure. The signs of Poisson's ratio can also change with the axial strain by rationally designing the microstructures. By combining curve fitting and curvature and parametric functions, the mechanical behaviors of lattices constructed by bioinspired microstructures can also be predicted. The lattice structures are then demonstrated to reinforce a hydrogel with modulus increased by around 2 orders and act as a biomimetic soft-strain sensor. This work could aid the design of a hierarchical lattice and have potential applications in tissue engineering, stretchable electronics, and soft robotics.