Physics-based discrete models for magneto-mechanical metamaterials

Magneto-mechanical metamaterials are emerging smart materials whose mechanical responses can be tailored through structure architecture and magnetic interactions. The latter provides additional freedom in the material design space and leads to novel behaviors due to its nonlocal nature. The enriched functionalities open new possibilities in various applications, such as actuators, energy absorbers, and soft robots. However, the nonlinear and nonlocal coupling between elastic and magnetic forces poses a great challenge in the modeling and simulation of these systems, further hindering theory-based rational design strategies. Here, we focus on a class of magneto-mechanical metamaterials comprising elastic solids embedded with rigid permanent magnets. The clear separation between elastic and magnetic forces simplifies the design and fabrication process, yet their nonlocal interplay still allows for complex behaviors. We present a simulation framework for such magneto-mechanical metamaterials by combining a lattice spring model for the elastic solid with the dipole model for the magnetic interactions and implementing it in the LAMMPS molecular dynamics software. We demonstrate the capabilities of our framework by simulating a few representative structures, including shape-locking lattice metamaterials, a soft cellular solid with controllable buckling, and a metamaterial chain with phase-transforming behavior. For the shape-locking lattice metamaterials, we successfully capture the magnetic-actuation-driven reconfiguration and the nonlinear mechanical response of the curved lattices. For the soft cellular solid, we identify its buckling patterns under external non-uniform magnetic fields and simulate a buckling evolution process consistent with experiments. For the metamaterial chain, we include the strong long-range interactions among the embedded magnets and reproduce the controllable phase transitions in the experiments. Our work provides a simple yet versatile simulation methodology to investigate the nonlinear mechanical behaviors in the presence of strong external and internal magnetic forces, which will facilitate the design and analysis of magneto-mechanical materials. It can also be applied to other magnetically-driven smart structures, such as soft robots.