Nonlinear elastodynamics of dilational metamaterials

Architected structures such as checkerboard patterns of squares joined by thin ligaments at their corners are capable of nonlinear deformations in which the structure contracts globally in the plane while individual elements counter-rotate. However, recent work shows that under generic driving such structures display a wide variety of nonlinear waves rather than this single global mode. We show that such excitations can be understood in terms of conformal symmetry, in which a wide variety of nonlinear (conformal) deformations are nearly degenerate in energy. This symmetry leads to low-energy surface waves whose dispersion is controlled by the structure's bulk modulus and by the size of the architected unit cell. Simulations and experiments also provide evidence of new conserved quantities, the spatially complex generalizations of linear and angular momentum. This approach provides a new platform for creating and controlling novel nonlinear waves for energy harvesting, sensing, and mode conversion. Conformal symmetry grants a degree of analytic control and predictability for characterizing novel waves in complex structures. [Work supported by Army Research Office (MURI # W911NF2210219)]