Modeling Theory With High Efficiency And High Accuracy For Electromagnetic Sheet Metal Forming Process

Electromagnetic forming as one of the high-velocity and high energy rate forming methods,which has properties of short forming time and large forming forces,can highly improve forming limits,retain wrinkles,and decrease the springback.In addition,it is environmental-friendly and it shows great applicability.Numerical simulation technique centered as the finite element method is the indispensable technological means for designing of plastic processing.However,the computational accuracy is very low when using unstructured meshes such as triangular and tetrahedral element.It is hard for pre-processing when using structured mesh based method such as quadrilateral and hexhedral elements which own high computational costs and low mesh distortion resistance.It is a great significance for improving technology and promoting industrialisation of electromagnetic forming to build a high accuracy and efficiency numerical model.This thesis analyzed the electromagnetic forming characteristics with the novel numerical method,and focused on the research of key theory and method for coupled electromagnetic and mechanical field problem on electromagnetic forming process.It is dedicated to establish a high accuracy and efficiency numerical modeling theory for electromagnetic forming.Main work includes the following aspects:1.Novel triangular shell element for sheet metal stampingA 3-node shell element based on Mindlin-Reissner theory and discrete shear gap is presented,in which discrete shear gap of each field node is deduced using rotations of all three field nodes in local coordinate system by the integral from the fictitious central point to corresponding field node which makes it alleviate the shear locking phenomenon.Dynamic solution has been deduced for sheet metal stamping.It is very efficient and stable for sheet metal stamping when combining several material constitutive models.2.Electromagnetic forming modeling theory based on unstructured meshesConsidering the superiority of unstructured meshes in discretizing complex geometries,this thesis proposed an edge-based smoothed finite element method for electromagnetic field problem by using gradient smoothing technique.It can improve the computational efficiency since linear interpolation is adopted in this method.Meanwhile,it can highly improve the accuracy of low order element in solving eddy current problems.It is a competitive numerical method for electromagnetic fieldproblem with high accuracy and efficiency.3.Electromagnetic forming modeling theory based on unstructured meshesElectromagnetic forming can be seen as a coupled electromagnetic and mechanical problem.Governing equations for eddy current analysis and dynamic large deformation analysis are established under the solution scheme of edge-based smoothed finite element method.Dynamic moving mesh and re-meshing techniques are employed for updating air meshes to decouple the coupled field.Iteration coupling is utilized to consider the interaction between electromagnetic and mechanical field.A set of theory for modeling electromagnetic forming based on unstructured meshes have been proposed.Several numerical examples including tube expansion,tube compression and sheet metal free bulging have been analyzed to validate the feasibility of present method.The present method can simulate the electromagnetic forming process accurately.4.Electromagnetic forming modeling theory based on solid and shell interactive mapping elementIn order to improve the computational efficiency of electromagnetic forming,axisymmetric shell element and triangular shell element are employed for axisymmetric and three dimensional dynamic large deformation analysis,respectively.Meanwhile,a six-node triangular prism element based on cell-wise gradient smoothing technique is proposed for linking triangular shell element in three dimensional problems.The triangular shell element and triangular prism element can be interactively mapped through extracting the mid-surface of prism element and draping over the nodal normal direction,respectively.The nodal data can be transferred from one field to the other.Several practical electromagnetic forming examples have been analyzed.A solid and shell interactive mapping method with high efficiency and accuracy for electromagnetic forming has been established,which can highly improve the efficiency without lose of accuracy.Additionally,electromagnetically assisted stamping can be seen as a hybrid forming technique that combines electromagnetic forming into quasi-static conventional stamping.The triangular prism solid and shell interactive mapping element builds a bridge between conventional stamping and electromagnetic forming process,in which shell element is employed in conventional stamping process and dynamic large deformation analysis of electromagnetic forming.A linear six-node prism element is developed for transient eddy current analysis in electromagnetic field of electromagnetic forming process.The proposed numerical modelling cansuccessfully simulate the combined quasi-static-dynamic process.5.Phase field fracture model for predicting cracking problem on forming processIn order to explore the feasibility of phase field fracture applied for predicting cracking problem on forming process,an n-sided polygonal smoothed finite element method with non-matching meshes based on gradient smoothing technique is presented for phase field fracture modelling.Non-matching meshes are employed for local refinement to satisfy the mesh size requirement on phase field fracture model.The feasibility and efficiency have been validated by several brittle fracture examples.Then,a staggered scheme for decoupling displacement and phase field is developed in commercial software ABAQUS by using user defined material(UMAT)and user defined element(UEL)subroutines.Elasto-plastic material is taken into account for predicting crack propagation.Last,phase field model is embedded into explicit dynamic large deformation scheme.A combined explicit-implicit solution scheme is developed for dynamic large deformation analysis and evolution of phase field.The model is applied for predicting cracking problem on forming process.It opens up the applications of phase field fracture model.