Multi-scale Modeling And Simulation On Buckling And Wrinkling Phenomena

Instability phenomena have been widely observed in the engineering field.When a structure is subjected to compressive stress,buckling may occur.The occurrence of wrinkles may pose a limit on the performance of materials or structures and are always thought to be avoided,but nowadays may find some applications in measuring and designing the mechanical properties of materials and structures.For these reasons,it is quite necessary to study the occurrence and evolution of wrinkles in a structure in an accurate and efficient way.Generally,the instability phenomena have two typical characteristics:1)the in-stability pattern is nearly spatially periodic,and 2)the wavelength of the wrinkles is very small compared to the structural size.Compared with the experiment,numerical simulation for this kind of phenomena can significantly save time and economic cost,but now faces two challenges:1)to take into account both computational efficiency and accuracy is difficult,and 2)to pilot the nonlinear simulation is challenging because too many solution paths exist around the useful one.The main aim of this thesis is to develop advanced and efficient multi-scale mod-eling and simulation techniques to study the instability phenomena in three common engineering structures,i.e.,membrane,film/substrate and sandwich structures,by com-bining the Technique of Slowly Variable Fourier Coefficients(TSVFC),the Bridging Domain Method(BDM)and the Asymptotic Numerical Method(ANM).Towards this end,based on the Von Karman plate equations,the TSVFC has been firstly used to develop a two-dimensional(2D)Fourier double-scale model for membrane,which has also been implemented into commercial software ABAQUS via its user-defined el-ement(UEL)subroutine.Then a 2D Fourier double-scale model is constructed for film/substrate.Further,making use of the deformation features of the film/substrate,a one-dimensional Fourier double-scale model is developed by using both the TSVFC and the Carrera's Unified Formulation(CUF).Subsequently,based on high-order kine-matics belonging to Zig-Zag theory,a 2D Fourier double-scale model is deduced for sandwich plates.The governing equations for the above models are discretized by the Finite Element Method(FEM),and the resulting nonlinear systems are solved by the efficient and robust nonlinear solver ANM.In addition,a bridging domain method(Ar-lequin method)is implemented into ABAQUS with a simpler formulation to construct a 2D multi-scale model.These double-and multi-scale models are then adopted to study the instability phenomena emerging in the above three kinds of structures subjected to different external loads(e.g.,uni-and bi-axial compressive stresses).Results show that the established models in this paper could accurately and efficiently simulate various instability phenomena.Besides,it's found that the membrane instability is very sen-sitive to the boundary conditions,and there exists a dimensionless parameter that is almost constant near bifurcation point for various boundary conditions,loading cases and geometric parameters.This parameter may be quite helpful for fast predicting the occurrence of wrinkles.The results of this thesis are proved to accurately and efficiently predict,prevent and utilize buckling and wrinkling of membrane,film/substrate and sandwich struc-tures,and also hoped to lay a foundation for the study of other instability phenomena with nearly periodic patterns.