A multi-scale variational asymptotic model for the effective performance of sandwich beams

In order to effectively analyze the properties of sandwich beams, a multi-scale variational asymptotic model was established based on the variational asymptotic method. Firstly, the geometrical nonlinear equations of the original 3D sandwich beam were established based on the concept of rotation tensor decomposition. By using the characteristics of slender and heterogeneous, the anisotropy and heterogeneity problems of sandwich beams were strictly decomposed into 1D nonlinear analysis along the beam reference line at the macroscopic level and unit cell constitutive analysis at the microscopic level. Based on the principle of minimum potential energy, the effective stiffness and fluctuation function solution were obtained by minimizing the variational leading items in the strain energy functional, and substituted into the 1D model of beam to perform the global response analysis. Then, the resulting global response and fluctuation function solution were used to recover the local fields. Due to the variational characteristics, the constructed multiscale model can be easily numerical implemented by finite element method. The example results of three kinds of sandwich beams show that the global displacements and local stress fields obtained by the constructed model are in good agreement with the 3D finite element method, but the computational cost and modeling workload are significantly reduced, which provides a simple way for the structural designer to evaluate the performance of the sandwich beams at the initial design stage.