Modeling and design of 3D printed hyperelastic lattice metamaterials with bionic S-shaped stress-strain behaviors

Lattice metamaterials made of stiff polymers, ceramics, and metals have been extensively designed to reproduce the mechanical behaviors of biological tissues, holding promising applications in biomedical devices and tissue engineering. However, lattice metamaterials composed of soft materials have been far less explored due to challenges posed by material nonlinearity and large deformations. Here, hyperelastic lattice metamaterials with curved microstructures are fabricated by 3D printing elastomers and are developed to mimic bionic S-shaped stress-strain behaviors. We propose a design framework for 3D printed hyperelastic lattice metamaterials that integrates digital geometry generation, hierarchical mechanics modeling, and validation by finite element (FE) simulations and experiments. The microstructures are modeled through deriving a Timoshenko-type beam theory governed by hyperelastic strain energy potentials. The model is then combined with the deformation and equilibrium analysis considering non-rigid connections between microstructures to predict the mechanical responses of hyperelastic lattice metamaterials. Using the developed design framework, programmable S-shaped stress-strain behaviors and high fracture strains (over 800%) are achieved. We demonstrate S-shaped stress-strain curves that match skeletal and cardiac muscles and highly stretchable lattice sensors for remote controls. This study provides design methods and theoretical guidelines for hyperelastic lattice metamaterials, holding promise for robotic sensors with bionic performance and functionality.