Linear strain gradient-regulated bifurcation of circular bilayer plates

Bilayer structures with controllable self-folding capability have found applications in a variety of cutting-edge fields such as flexible electrics, wearable devices and soft robotics. The folding of bilayer structures occurs when the mismatch strain between the two layers exceeds the bifurcation threshold, resulting in a deformation transition from an axisymmetric to a folded state. Previous efforts have predominantly focused on bilayer structures with uniform and/or anisotropic strain distributions. However, the role of non-uniform in-plane strain distributions in regulating the bifurcation of bilayer structures has not been fully understood. In this study, the effects of linear in-plane strain gradients on the bifurcation of circular bilayer plates, both with and without geometric mismatch, are systematically investigated by combining theoretical analysis, finite element simulations and experiments. Our results reveal that both the mismatch strain gradient and the geometric mismatch between the two layers play crucial roles in regulating bifurcation. Notably, linear mismatch strain gradients with larger strain at the center delay bifurcation, while those with larger strain along the edge promote bifurcation. This work offers new insights into the design of controllable self-folding bilayer structures, which is of great significance for advanced applications.