Symplectic analysis for wrinkles a case study of layered Neo-Hookean structures

Wrinkles are widely found in natural and engineering structures, ranging from skins to stretchable electronics. However, it is nontrivial to predict wrinkles, especially for complicated structures, such as multilayer or gradient structures. Here, we establish a symplectic analysis framework for the wrinkles and apply it to layered neo-Hookean structures. The symplectic structure enables us to accurately and efficiently solve the eigenvalue problems of wrinkles via the extended Wittrick-Williams (w-W) algorithm. The symplectic analysis is able to exactly predict wrinkles in bi- and triple-layer structures, compared with the benchmark results and finite element simulations. Our findings also shed light on the formation of hierarchical wrinkles