Arc-Length Based Inverse Finite Element Approach And Its Applications In Sheet Metal Forming

Blank design is important in sheet metal stamping forming process.It is the premise to obtain the blank shape of forming parts to analyze forming distortion degree,design technology as well as draft process specifications.Reasonable blank shape and size can obviously improve the inhomogeneous deformation of blank and fully exploit the metal forming performance.Among the methods of blank design,the Inverse finite elements Approach(IFEA)based on total strain theory,only considering the initial and final stages of the parts,makes IFEA method very fast and high effective.Under some specific conditions,IFEA method can quickly calculate blank shape,final stress,strain,thickness change rate etc.In the paper,the basic theory of sheet forming is fully studied.The basic theory of IFEA and how to operate it are briefly introduced.Then the anisotropic constitutive relation under proportional loading condition and flat triangular membrane elements of constant thickness having three nodes are adapted,and then the related formula is put forward and the related computer program is implemented.Then we get the solutions of IFEA non-linear equations by the ABAQUS user define element option (UEL) and it's standard calculator.The key problem of IFEA is the calculation of initial solutions,because of the difficulty to keep the topology of mesh elements.So the initial solutions not only influence the rate of convergence but also determine the results of IFEA are valid or not.Arc-length method is proposed to resolve the difficulty,which map the final product by the arc length of every node of product to the original node.This method can keep topology of all the mesh elements and improve the convergence of IFEA.Cylindrical cup and door-like product are simulated by IFEA program.Then the results are compared with those simulated by incremental soft ware DYNAFORM and experimental.The comparisons show that inverse approach,which can be used to evaluate the sheet metal forming process quickly,is an effective approach for blank design.So it is a good choice to use this method in the initial stage of die design.Finally,the IFEA based on the four-node isoparametric element is discussed after the triangular membrane element and part of the finite element equation is established in this paper.Then the initial solution of four-node element is obtained by arc-length method,which is the basic of IFEA based on the four-node element.