# ANSYS/LS-DYNA simulated stamping, forging and casting

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The following only on the LS-DYNA in the simulation of stamping, forging and casting process of the functions and characteristics of the process are described:
1. the physical description of the Stamping Process of the sheet metal is: under the Joint Action of various parts of the mold (usually the punch, die and die-pressing board), the sheet metal is greatly deformed, the deformation of the sheet metal can come from forcing the external work of the die component, and the energy transmission is completely dependent on the contact and friction between the mold and the sheet metal. It can be seen that the simulation of the forming process, the theory and accuracy of the contact algorithm of the software determine the reliability of the program. In addition, due to the great displacement and deformation of the sheet, the unit type used to simulate the sheet metal should meet this requirement. Make certain assumptions: the mold is a rigid body, and the movement of the mold can be directly used as the displacement boundary condition of the stamping system. The physical model of the stamping process is transformed into a mechanical model, that is, the momentum equation, the boundary condition, and the initial condition. The displacement function of the sheet metal is obtained under the given mold displacement condition, and the momentum equation, boundary condition, and initial condition are satisfied at any time. This is a general mechanical problem and can be solved using the finite element method. The die is defined as a rigid body when the LS-DYNA is analyzed for stamping, so both the sheet and the die are separated by Shell units. All the units of the LS-DYNA are described by using the method of increasing the resource length. There are a total of 16 shell unit algorithms, which can be used for Board Forming analysis. There are 11 units, which can be classified as four-node and three-node units; single point credits, multi-point credits, and select-distinct CED credits. The unit adopts the deformation and rigid motion in the motion of the separation unit in the co-rotational coordinate system. You can obtain reliable results when using single point credits. When the warpage and bending deformation of a unit are large, the precision can be ensured by increasing the number of integral points along the thickness of the shell. The material model used for sheet metal forming is a variety of elastic-plastic materials, which can take into account the characteristics of the undirected and reinforcing. Reinforcement types include exponential reinforcement, follow-up reinforcement, equidirection reinforcement, hybrid reinforcement, and the effect of strain rate on material reinforcement. The effects of strain rate are classified into two ways: 1. Cowper-Symonds model and 2. The stress-strain curves under any strain rate are given in a table. Some material modes reference the transition hypothesis of hill or barlat, and assume the plane stress state of the shell unit, so it is almost dedicated to plate forming simulation. In addition, the flow limit dia. of the given material can be used to determine the partial cracking of the sheet during the pull delay process. At present, there are more than 30 contact types for LS-DYNA, 12 are suitable for Plate Forming analysis, all adopt the penalty function method (penalty), and consider the shell unit thickness and its variation in the contact calculation process. It is worth noting that: 1. Contact-drawbead (contact-drawbead) can be considered as a non-linear spring algorithm. A curve of resistance variation on the sheet metal should be given for each unit length. 2. Three new contact types (forming type contact) are added to the LS-DYNA for plate forming simulation. These contact types Reduce the continuity requirements for the mold mesh and increase the computing speed. 3D adaptive mesh can be used for Plate Forming Analysis of LS-DYNA. Partial encryption can be performed on the sheet mesh During calculation. The principle of grid encryption can be: 1. thickness variation; 2. curvature change; 3. the penetration depth of a single step.
2. The Forging Process is a mass Forming Process of metal. Compared with plate forming, the physical description is the same as that in the mechanical model, but the unit, material, and mold definitions are different. In the forging process, the deformation of the mold is often considered. The unit adopts a solid unit. In most cases, the material has undergone a large temperature change and is a thermoplastic material. The entity units of LS-DYNA can be divided into three categories: 1. structural units; 2. Ale units (including Euler fluid units); 3. Acoustic units. Structural solid units should be used for forging analysis. These units can be divided into single point points, multi point points, and reduced points (select-reduced CED) units; nodes with degrees of freedom of rotation (nodal rotations) and the number of degrees of freedom without rotation. The Unit uses the co-rotational coordinate system to separate the deformation and Rigid Body Motion in the unit motion, and uses jaumann stress rate in the stress update to avoid the stress generated by the rigid body motion. When the shear deformation is large, you can choose to use green-naphdi stress rate. The deformation structure unit is 8 nodes and 6 planes, which can be converted into 6 nodes and 5 planes or 4 nodes and 4 planes. The thermoplastic material of the LS-DYNA can be divided into 7 segments by listing the properties of the material given at different temperatures, for example, a commonly used type of homogeneous thermoplastic material, different parameters such as elastic modulus, Poisson's ratio, yield stress, hardening modulus, and thermal expansion coefficient can be defined in each temperature segment. This material adopts linear hardening mode. The thermal properties of the materials (such as the specific heat and thermal conductivity) can be the same or the opposite sex. In the LS-DYNA, the definitions of structure materials and thermal materials are separated, and the related thermal contact interface is defined in the contact heat transfer analysis, so the coupling analysis of structure and thermal field can be carried out. In most forging analyses, as the metal forming process continues, the deformation of the initial mesh increases gradually, which will reduce the precision of the unit or even cause distortion. Therefore, the Grid re-division function (remeshing) must be used ). The following steps are involved in re-division of the grid: 1. check the deformation degree of the Grid. If the calculation is stopped after the specified deformation degree is exceeded, save the result. 2. check the nodes that need to be changed, adjust the node location, ensure that the material boundary remains unchanged, and the nodes inside the material can be freely moved. 3. Map the saved results to the new grid. 4. reinitialize and compute the grid. The LS-DYNA provides the re-partitioning function for two-dimensional and three-dimensional mesh. In addition, LS-DYNA has long been using a more advanced grid ale, that is, the concept of the Euler's grid. The purpose and process of the ale mesh rezoning are basically the same as that of the remeshing, but there is an essential difference in the mesh Description between the two (the latter is the Laplace mesh ). Combined with their respective advantages, Ale has been widely used in the extreme deformation of structural materials. The following is a detailed description of the ale technology.
3. as mentioned above, the structure unit Motion Description adopts the Laplace method. This is because the reference structure is always solved by the initial configuration, which is composed of the material point (material point, x 0 is the initial form of the total resource, and the reference configuration in the updated resource concept is the form of the previous integral step, that is, x n-1) to determine the momentum equation, motion-strain relationship, and strain-stress relationship. It can be seen that the integral points of any unit can remain unchanged throughout the process, that is, the same material point, which is extremely important for solving historical deformation problems, because for solid structure materials, this is exactly the case. For the fluid medium, the LS-DYNA is described by Euler, that is, the current configuration (usually recorded as spatial point X) to determine the momentum equation, deformation-strain relationship, strain-stress relationship, therefore, the integral points of the Step units are not the same material points, that is, the matter can be transmitted between the Euler mesh, and the pressure and energy are transmitted in the Euler's area due to the movement of the matter. The two methods are essentially the same, but they use independent variables (their independent variables are x, t, and x, t) they have different characteristics. In form, the mesh nodes of the former and the material point correspond to each other in the process of material movement, while the latter node does not move, and the material points move in the euler mesh. In the former, the history of any material point can be obtained. In the latter, only the characteristics of the material point at the Euler node at t time can be obtained, and the next time is the characteristics of another material point, however, it is difficult to determine where the materials at this node come from. In addition, in terms of physical description, there is a big difference between the Laplace and Euler in determining the momentum equation, the mass equation, and the energy equation. Generally, the Euler equation adopts a conservative form, however, the use of the Laplace equation is often simplified in engineering assumptions, which is particularly evident in the expression of the mass equation.
In short, Laplace and Euler are two kinds of descriptions of the motion of the continuous medium. Because of the different reference configurations (or the different positions of the observer ), as a result, the focus of observation and description of material movement is different. The ALE method was first proposed by Noh (1964) in terms of coupling Euler-Lago. By the end of 1980s and the beginning of 1990s, it formed a mature theory and appeared in a few analytical programs. In the ale description, the mesh point can be moved along with the object, but it can also be fixed in space, or even fixed in one direction, while moving along with the object in another direction. In ale, the division of Finite Elements refers to the reference structure. The mesh points are the reference points. The mesh is independent of the Motion of objects and spaces, that is, the reference structure is known, the initial and current configurations are to be solved. The arbitrary Laplace-Euler (ALE) method combines the advantages described by pure Laplace and pure Euler, and overcomes their respective shortcomings, it has become a very advanced and effective method for the analysis of medium deformation in nonlinear continuous media mechanics. As early as 91 years ago, The LS-DYNA program successfully introduced the ALE algorithm, it has been widely used in fluid dynamics, fluid-structure interaction, machining, collision, explosion impact, contact, and other big deformation problems, such as the tsunami, the dam's deciding port, the heavy shaking of the fluid in the container and the leakage of the liquid, the expansion of high-pressure bubbles in the liquid, underwater explosion, ultra-high-speed collision, forming charge, bird hitting aircraft, forging and so on. The ANSYS/LS-DYNA algorithm, in addition to Laplace and ale, also includes Euler's and multi-material fluid solutions. There are three main types of Euler's Arrays: first-order precision donor cell, second-order precision Van Leer, and second-order precision Van Leer + half index shift. The Unit configuration of multi-material fluids mainly includes two types: fluid + blank material and full blank material; mixing unit of various materials (pressure balance ). These models can be automatically coupled with common solid structural units such as solid, Shell, brick, and beam, without the need to slide the interface. At the same time, the addition of such solver makes ANSYS/LS-DYNA have the ability to compress fluid flow analysis, it can be used to solve complex fluids and fluids, such as free interface flow, wave breaking, any pipeline flow, fluid mixing, composite material injection molding, metal component casting, and high-speed and high-pressure gas injection- structure coupling problem. During Casting simulation, the cavity of the mold is defined as the Euler zone and the material is defined as void or any substance (such as air ), the gate unit is defined as the Euler ambient, that is, the material enters the Euler region, and the motive force of the material movement is pressure and (or) gravity. The fluid medium of LS-DYNA is defined as fluid power material. Its Properties mainly include density and viscosity, the pressure of the unit and the compression are determined by the attached state equation (the state equation is the pressure equation, its independent variables include density, temperature, and internal energy ). The pressure difference between the cavity and the gate gradually decreases as the material flows into the Euler's zone from the gate, and finally reaches the balance. The simulation can be terminated. The heat diffusion can be considered in the casting analysis, and the temperature boundary conditions and heat generation can be conveniently applied in the LS-DYNA. In short, the LS-DYNA time Integrator uses the central difference format to explicitly solve the unknown. Since the quality matrix is divided into two aspects, the solution speed can be further accelerated. For example, the general stamping, forging, casting and other problems reasonably control the finite element scale, running on the PC for 5-20 hours can achieve the ideal results, such efficiency is difficult to compare with other programs.

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