Morphology of non-Euclidean disks

The out-of-plane displacements of plates are influenced by factors such as nonuniform thermal expansion which corresponds the research of 3D deformation of elastomer controlled by the target metric in non-Euclidean plates. The well-known mass-spring model was used to simulate the deformation of disks driven by given swelling functions corresponding positive and negative target Gaussian curvature K. The evolution of waves under negative target Gaussian curvature was analyzed with different thickness t. The impact of swelling factor and strain gradient on the ratio of bending energy to strain energy was studied with the same thicknesses. The ratio transforms rapidly when the number of waves changes for K<0. Scaling of stretching and bending energy about thickness was obtained while dicks were driven by the same swelling function. Stretching and bending energy both vary like t2.5 with K>0, compared with t4 of bending energy in disks with K<0.