- Detail

Sheet metal forming simulation software

1. introduction

in the 1980s, a team composed of automobile manufacturing engineers and mold designers began the research and development of the innovative software, which comes from innovative deep drawing. As the name suggests, this is a special finite element numerical simulation and analysis software for metal deep drawing. At that time, explicit finite element method was very popular, especially when it involved highly nonlinear material response, finite deformation, and sudden changes in boundary conditions caused by complex contact problems. In view of the fact that sheet metal forming is a quasi-static process, engineers decided to use implicit algorithm in index; An obvious advantage is that it is convenient and accurate to calculate the springback. Nowadays, although explicit algorithm has many shortcomings and deficiencies in solving quasi-static problems, its representative software (such as LS DYNA) seems to have become dominant in the sheet metal forming numerical simulation market. This dominance is based on a widely circulated idea that implicit algorithms are not as reliable or efficient as explicit algorithms. However, although in many cases, the explicit algorithm can get satisfactory results, the implicit algorithm still has its outstanding advantages in the simulation application of sheet metal forming. Especially in the case of calculating the impact force and springback of sheet metal, the result of implicit algorithm is more reliable. As new materials such as ultra-high strength steel, dual phase steel and special aluminum alloy are constantly used, its simulation calculation becomes more and more important

in the research and development of index, engineers focused on the quality of analysis results for more complex working conditions, such as accurate rebound calculation and impulse pressure calculation. Therefore, the implicit solution method is adopted by index, and an original special shell element is used. This element has an additional degree of freedom in the thickness direction. The leading material model is used, and the deformation gradient of the material is decomposed into elastic and plastic parts by multiplication. These technologies have laid the foundation of indeed, a high-end forming simulation software

in the past, when using implicit algorithm to solve problems, it is often necessary to use high-performance computers because the finite element model is very large. Now, due to the new finite element technology based on domain decomposition, the calculation speed of implicit algorithm has been greatly improved. This is good news for small companies that need to calculate large-scale forming simulations and are unwilling to buy expensive vector machines and mainframes. In recent years, the R & D team of index has launched feti-index, which is a parallel version of index based on FETI (fine element teaching and interconnecting) domain decomposition technology. Feti-index follows the MPI standard (Message Passing Interface) and can run on heterogeneous hardware platforms or homogeneous platforms such as Linux clusters, which are becoming more and more important in the automotive industry

as the implied meaning of the name "index", index is committed to the digital simulation of deep drawing problems. Now, indexed has covered almost all metal forming simulation fields from bending, rolling, flanging, bonding to collision, hydraulic, hydraulic deep drawing and so on (as shown in Figure 1)

Figure 1: application field of index

in addition to the above high-precision methods, index also integrates specially designed membrane units, so that users can quickly evaluate the forming process roughly

the following part of this article will mainly describe the main features of the indexed software. The focus is on the original shell unit and material model of index, which are the special features of index. In addition, the implementation method of FETI is described, and then the simulation example of feti-index is shown, in order to further understand the scalability of this method

2. The characteristics of index

2.1 integration scheme

when using explicit finite element methods such as LS DYNA or PAM-STAMP to simulate deep drawing, in order to save calculation time, it is usually necessary to enlarge the speed of the forming process and (or) the surface of the sheet in contact with the specimen to adopt the density of sticky soft rubber. The first method is to reduce the simulation time, and the second method is to increase the so-called critical time steps, so as to reduce the total number of time steps. These methods will inevitably lead to dynamic effects that are not consistent with the actual process. For example, the value of impulse pressure will be exaggerated; It will be found that only elastic deformation occurs in the actual process, while plastic deformation occurs in the simulation results. Because of this situation, extra care must be taken when analyzing the results of explicit deep drawing simulation. Mastering this explicit algorithm naturally requires a lot of mechanical background knowledge and rich computing experience. These requirements are too high for mold designers who only need digital simulation on specific problems. In order to avoid changing some parameters in order to improve efficiency and eliminate the dynamic response that is inconsistent with the actual results, the implicit algorithm is adopted by index, and the equilibrium iteration is carried out at each incremental step

in the explicit simulation of the forming process, it usually takes hundreds of thousands of time steps, while when using the implicit simulation of indexed, it takes about 100 to 200 incremental steps. Of course, this depends on the nonlinearity of the problem. The explicit integration method avoids the assembly of the element stiffness matrix and the solution of the corresponding system equations. In order to improve the efficiency of solution, it is necessary to minimize the number of operations required in each time step. In the explicit algorithm, there are three most time-consuming operations, the first is the solution of the constitutive equation, the second is the element algorithm, and the third is the contact search. In order to improve the efficiency of explicit finite element algorithm, software developers tend to simplify these processes as much as possible. For this reason, only the simplest constitutive equation and the most primitive element algorithm, namely the belytschko Tsay shell element, are usually used in the explicit algorithm. For the same reason, explicit algorithms usually use few integration points in the thickness direction of shell elements

in implicit algorithm, compared with solving huge linear equations, the influence of model change on calculation time can be said to be negligible. Choosing a relatively complex material model or a finite element model that requires a lot of calculation on the finite element will not have a great impact on the efficiency of the implicit algorithm. Even increasing the integration point in the thickness direction has little effect on the solution speed of implicit forming simulation

2.2 unit

included integrates solid unit, shell unit and membrane unit, which can cover all forming simulations. Users can choose a faster membrane element algorithm or a more accurate shell element. Using the membrane unit, we can get a result caused by the insulation layer of wires and cables, because the bending characteristics of the membrane unit are only obtained through geometric relations rather than physical relations. The film characteristics and bending characteristics can be calculated independently, so a faster iterative equation solver can be used. For the first evaluation of the forming process, or when repeatedly improving the geometry of the die or some parameters of stamping, membrane elements can generally be used. Using membrane element, it has enough accuracy in thinning, material flow and wrinkle prediction. However, if more accurate calculation results are needed, such as accurate punching force or springback, or the last forming process verification, we still recommend the use of shell element. This unit is specially developed for the indexed software. It meets the following requirements:

· good bending and film properties

· it can deal with material and geometric nonlinearity

· can handle double-sided contact

the shell element based on the traditional shell theory is not suitable for describing double-sided contact, because this theory adopts the plane stress hypothesis（ σ 33 = 0), thickness changes are often ignored（ ε 33 = 0）。 In the real metal forming process, the normal stress in the contact area between the sheet and the die is not zero, and the thinning effect caused by the large film strain has a great impact on the contact area, thus affecting the friction distribution on the blank, so they should not be ignored [1]

in order to overcome the shortcomings of traditional shell elements, Professor schoop [2] proposed a special shell element theory - guided shell theory, which was implemented in the first edition of index [3] in 1989. In the following 15 years, in order to reduce the locking effect and improve the convergence, many improvements have been made to the original indexed shell unit. When it is necessary to obtain accurate punching force and predict the springback characteristics of sheet metal, the advantages of this kind of shell element of index are obvious compared with those used in other sheet metal forming simulation software, especially those based on traditional shell theory

in the new version of index (v8.0), a new shell unit is added. This element is specially designed to meet the requirements of high-precision Springback Analysis. It is based on the improved guided shell theory [4] and can be used as an alternative to the previous shell element. Like the previous shell element, it is a 3-node element with 21 degrees of freedom, and each node has 7 degrees of freedom. The physical meaning of these degrees of freedom is as follows:

represents the three components of the position vector of the lower surface at the finite element node n

ux1n, ux2n, ux3n represents the three components of the position vector of the upper surface at the finite element node n

α N additional degrees of freedom, mainly considering the offset between the middle surface of the material and the geometric middle surface of the sheet during the bending deformation of the element

Figure 2: schematic diagram of the indexed shell element with double-sided contact and additional degrees of freedom in the thickness direction

due to the seventh degree of freedom α， The straight-line hypothesis can be expressed in the following form

where x is the position vector of any point in the shell element, R is the position vector of the middle plane, and d = (UX LX)/t is the indicator in the fiber direction. Z is the coordinate of the fiber direction. T represents the initial cell thickness. It is easy to draw from the above equation that the distance between the geometric mid plane and the material mid plane is equal to 8 times the seventh degree of freedom α。

for the traditional finite element method, the position vector in the element body is obtained by shape function interpolation. By partial differentiation of the position vector of the actual geometry, that is, the geometry after element deformation, the deformation gradient f can be obtained relative to the initial position or the element reference configuration, from which several measures of strain can be calculated. The new shell element of index is a kind of incompatible shell element. Only the constant deformation gradient F0 relative to the mid plane of the element is obtained by the above method. The stress values outside the plane in the element are obtained by interpolation, which means that they do not necessarily match the given element displacement field (assuming strain theory)

for this new shell element, there are the following assumptions:

a) on the basis of Kirchhoff shell theory, the curvature of the element is linearly distributed

b) the transverse shear strain is calculated from the variable part of curvature by the equilibrium equation q = t M

c) relative to the triangular element plane formed by the deformed element nodes, the direction of curvature and transverse shear strain is not perpendicular to it, and the scalar product fo DN is the discretization of bending and shear deformation

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