Dynamic behaviour of 2D film-substrate structure with checkerboard regime via Symplectic Runge-Kutta method
Stretchable inorganic electronics,based on buckling mechanisms,have been fabricated.However,these electronics need to work in a dynamic environment and the dynamic behaviour of these structures is also one of important considerations for their applications in industry.In this paper,the potential energies due to bending and in-plane membrane deformation of the 2D film,and the kinetic energy and the potential energy of the compressed substrate of a film-substrate structure are formulated;then,by using the Lagrange equation,the governing equation of this buckled structure his derived.Since the analytical solutions of this equation cannot be obtained,it is solved by the Symplectic Runge-Kutta method.Through the numerical examples,it is found that the Symplectic algorithm can preserve the characteristics of the film-substrate structure in long-time,and also maintain the buckling characteristics,and thus provides an excellent numerical analysis method for determining dynamic behaviour of stretchable inorganic,buckled film-substrate-based electronics.
万方数据
维普
