Rational design of hyperelastic semi-linear material and its application to elastic wave control

Incremental elastic wave in a hyperelastic semi-linear (SL) material can be purposely controlled by pre-deformation with help of hyperelastic transformation (HT) theory. However, this material model, assuming a linear stress-strain relation for large deformation, has neither been realized with naturally occurring materials nor through microstructure design. By balancing the stiffness of axial and rotational springs in a hexagonal mass-spring lattice, we propose a lattice prototype to realize the SL material. The performance of the model is systematically verified from static strain energy to wave property on different finitely deformed configurations. Based on this SL lattice, an elastic wave cloak is designed and validated through numerical simulation. This work provides the first two-dimensional (2D) microstructure model for realizing SL material and paves the way for elastic wave control with HT method.