Dynamics Analysis of Topological Bistable Maxwell Lattices

Recent advances in mechanical metamaterials and topological phases have given rise to topological mechanical metamaterials that exhibit attractive topological properties to enable promising applications such as vibration isolation and free motion of structures. A topological Maxwell lattice, for example, appears to have zero-energy floppy modes on the soft edge, resulting in obvious differences of surface stiffness between the soft and hard edges. These zero modes lead to complicated motions of the lattice when various types of external loads are applied to the lattice. However, most studies on impact effects on the lattice used quasi-static mechanics in the linear regime. To address this issue, springs are added on the Maxwell lattice to achieve bistability, and to remove redundant degrees of freedom to generate predictable motions of the lattice. To characterize the deformation of a 2D bistable Maxwell lattice, all nodes in the unit cells that form the lattice are solved using Lagrange’s equations by considering the potential energy and the kinetic energy in the system. Energy dissipation due to friction is also considered for modeling the real material. The model is indicated to track the motion of the lattice under impact forces and to show the stress/strain distribution of the lattice in the time-space domain. Various loading and boundary conditions of the lattice are studied to examine how the Maxwell lattice can be programmed to dissipate the energy. The new findings can improve the design of topological Maxwell lattice and provide the prediction on the impact tolerance of any given configuration of the lattice.