New Stability and Equilibria of 2D Metamaterials of Bistable Elements

Geometric frustrations occur when elements in a lattice are subjected to conflicting boundary conditions which destroy the local order of the system. Here, we examine 2D triangular lattices of bistable elements to understand the origin and impact of geometric frustration. The formation and stability of complex ordered patterns is investigated both theoretically and experimentally. Experimental results present the stable configurations of square and triangular lattices of buckled beam-columns. Numerical continuation techniques are then used to explore the creation, destruction, and bifurcation of stable and unstable equilibrium configurations. Lastly, we consider the dynamic implication of frustrations within the 2D metamaterials of bistable elements. This work advances the understanding of the origin and role of frustration in mechanical metamaterials with applications towards characterizing frustrations in analogous systems such as the spins of neighboring particles or frustrations found in crystalline structures.