Wrinkling in graded core/shell systems using symplectic formulation

Abstract

Wrinkles in flat graded elastic layers have been recently described as a time-varying Hamiltonian system by the energy method. Cylindrical core/shell structures can also undergo surface instabilities under the external pressure. In this study, we show that by treating the radial direction as a pseudo-time variable, the graded core/shell system with radially decaying elastic properties can also be described within the symplectic framework. In combination with the shell buckling equation, the present paper addresses the surface wrinkling of graded core/shell structures subjected to the uniform external pressure by solving a series of ordinary differential equations with varying coefficients. Three representative gradient distributions are showcased, and the predicted critical pressure and critical wave number are verified by finite element simulations. The symplectic framework provides an efficient and accurate approach to understand the surface instability and morphological evolution in curved biological tissues and engineered structures.