Efficient implicit finite element analysis of sheet forming processes

The computation time for implicit finite element analyses tends to increase disproportionally with increasing problem size. This is due to the repeated solution of linear sets of equations, if direct solvers are used. By using iterative linear equation solvers the total analysis time can be reduced for large systems. For plate or shell element models, however, the condition of the matrix is so ill that iterative solvers do not reach the huge time‐savings that are realized with solid elements. By introducing inertial effects into the implicit finite element code the condition number can be improved and iterative solvers perform much better. An additional advantage is that the inertial effects stabilize the Newton–Raphson iterations. This also applies to quasi‐static processes, for which the inertial effects finally do not affect the results. The presented method can readily be implemented in existing implicit finite element codes. Industrial size deep drawing simulations are executed to investigate the performance of the recommended strategy. It is concluded that the computation time is decreased by a factor of 5 to 10. Copyright © 2003 John Wiley & Sons, Ltd.     

Mesh adaptive finite element formulation for moisture transfer in materials with a critical moisture content

Wetting or drying of most open porous building materials is characterized by a sharp moving waterfront. Due to the high moisture gradients at the waterfront, an accurate finite element simulation requires a very fine mesh. To reduce computational costs a mesh adaptive method based on the Arbitrary Lagrangian Eulerian (ALE) technique is proposed. To continuously relocate the nodes on the computational domain a remesh‐indicator is equally distributed. In problems of water imbibition or drying of open porous building materials specific attention has been paid to the zone of critical moisture content. To this extent the traditional jump‐based indicator, quantifying the jump of a selected state variable, has been modified into an area‐based remesh‐indicator. An error analysis of an academic example shows that the area‐based indicator is superior to the jump‐based one. To illustrate the capabilities of the remeshing method based on an area‐based indicator, one and two‐dimensional examples of water imbibition of ceramic brick and drying of cellulose fibre cement are included. Copyright © 1999 John Wiley & Sons, Ltd.     

Coupled thermo-mechanical analysis of metal-forming processes through a combined finite element–boundary element approach

This paper presents a new approach for obtaining the distribution of temperature in the dies during thermo-mechanical numerical analysis of metal forming problems. The proposed approach is based on a solution resulting from the combination of the finite element method with the boundary element method. The finite element method is used to perform the numerical modelling of the thermo-mechanical deformation of the workpiece, taking into account the geometrical and material non-linearities as well as the influence of the temperature distribution on the mechanical behaviour of the material. The boundary element method is applied for computing the distribution of temperatures in the dies. The combination of the two numerical methods is made using the finite element solution of the heat flow exchanged across the die–workpiece interface to define the boundary conditions to be applied on the thermal analysis of the dies. A numerical example of compression under plane-strain conditions is included to show the applicability of the proposed approach. © 1998 John Wiley & Sons, Ltd.     

A finite element model for thermomechanical analysis of sheet metal forming

A thermal model based on explicit time integration is developed and implemented into the explicit finite element code DYNA3D to model simultaneous forming and quenching of thin‐walled structures. A staggered approach is used for coupling the thermal and mechanical analysis, wherein each analysis is performed with different time step sizes. The implementation includes a thermal shell element with linear temperature approximation in the plane and quadratic in the thickness direction, and contact heat transfer. The material behaviour is described by a temperature‐dependent elastic–plastic model with a non‐linear isotropic hardening law. Transformation plasticity is included in the model. Examples are presented to validate and evaluate the proposed model. The model is evaluated by comparison with a one‐sided forming and quenching experiment. Copyright © 2004 John Wiley & Sons, Ltd.     

A continuum Lagrangian sensitivity analysis for metal forming processes with applications to die design problems

A continuum sensitivity analysis is presented for large inelastic deformations and metal forming processes. The formulation is based on the differentiation of the governing field equations of the direct problem and development of weak forms for the corresponding field sensitivity equations. Special attention is given to modelling of the sensitivity boundary conditions that result due to frictional contact between the die and the workpiece. The contact problem in the direct deformation analysis is modelled using an augmented Lagrangian formulation. To avoid issues of non‐differentiability of the contact conditions, appropriate regularizing assumptions are introduced for the calculation of the sensitivity of the contact tractions. The proposed analysis is used for the calculation of sensitivity fields with respect to various process parameters including the die surface. The accuracy and effectiveness of the proposed method are demonstrated with a number of representative example problems. In the die design applications, a Bézier representation of the die curve is introduced. The control points of the Bézier curve are used as the design parameters. Comparison of the computed sensitivity results with those obtained using the direct analysis for two nearby dies and a finite difference approximation indicate a very high accuracy of the proposed analysis. The method is applied to the design of extrusion dies that minimize the standard deviation of the material state in the final product or minimize the required extrusion force for a given reduction ratio. An open‐forging die is also designed which for a specified stroke and initial workpiece produces a final product of desired shape. Copyright © 2000 John Wiley & Sons, Ltd.     

Optimal process design in non-isothermal,non-steady metal forming by the finite element method

A new approach to process optimal design in non-isothermal, non-steady-state metal forming is presented. In this approach, the optimal design problem is formulated on the basis of the integrated thermo-mechanical finite element process model so as to cover diverse objective functions and design variables, and a derivative-based approach is adopted for conducting optimization. The process model, the formulation for process optimal design, and the schemes for the evaluation of the design sensitivity, and an iterative procedure for optimization are described in detail. The validity of the schemes for the evaluation of the design sensitivity is examined by performing a series of numerical tests. The capability of the proposed approach to deal with diverse process parameters and objective functions is demonstrated through applications to some selected process design problems. © 1998 John Wiley & Sons, Ltd.     

On the modelling of complex 3D bulk metal forming processes via the pseudo‐concentrations technique. Application to the simulation of the Mannesmann piercing process

The modelling of complex 3D metal forming processes using the flow formulation, implemented via the pseudo‐concentrations technique, requires the development of robust computational strategies for dealing with the velocity and pseudo‐concentration boundary conditions in the zone where the blank–tools contact is developed. A new algorithm, designed to fulfil those requirements, is presented in this paper. The Mannesmann piercing process is a metal forming operation used in industry for manufacturing metal seamless pipes. The results of the Mannesmann process finite element simulation are particularly dependent on the accuracy and stability of the algorithm used to describe the contact boundary conditions between the forming tools and the blank. The validation of the finite element model is performed by comparing the numerical predictions obtained using the new algorithm with the results of industrial tests. Copyright © 2005 John Wiley & Sons, Ltd.     

Experimental and finite element simulation methods for rate-dependent metal forming processes

An experimental procedure and a finite element simulation method for rate-dependent metal forming processes are developed. The development includes the formulation of a tangential stiffness matrix for an axisymmetric solid finite element with four node, eight degree of freedom, quadrilateral cross-section. The formulation includes the effects of elasticity, viscoplasticity, temperature, strain rate and large strains. The solution procedure is based on a Newton-Raphson incremental-iterative method which solves the non-linear equilibrium equations and gives temperatures and incremental stresses and strains. Three examples are studied. In example 1, finite element simulation for the upsetting of a cylindrical workpiece between two perfectly rough dies is performed and the results are compared with alternative finite element solutions. In examples 2 and 3, both experimental and finite element studies are performed for the upsetting of a cylindrical billet and the forging of a ball, respectively. Annealed aluminium 1100 workpieces are used in both examples. For the finite element analysis, uniaxial compression tests are first performed to provide the material properties. The tests generate elastic moduli and two sets of stress-strain curves (quasi-static and constant strain rate), which are used to establish a rate-dependent material model for input. For both examples 2 and 3, comparisons between the experimental and finite element simulation results for the forming force vs. die displacement relations and also for the deformed configurations show good agreement. The versatility of finite element methods allows for displaying detailed knowledge of the metal forming process, such as the distributions of temperature rise, yield stress, effective stress, plastic strain, plastic strain rate, forming forces and deformed configurations, etc. at any instance during the forming process.     

A quadrilateral mixed finite element with two enhanced strain modes

An improved plane strain/stress element is derived using a Hu–Washizu variational formulation with bilinear displacement interpolation, seven strain and stress terms, and two enhanced strain modes. The number of unknowns of the four-node element is increased from eight to ten degrees of freedom. For linear and non-linear applications, the two unknowns associated with the enhanced strain terms can be eliminated by static condensation so that eight displacement degrees of freedom remain for the proposed element, which is denoted by QE2. The excellent performance of the proposed element is demonstrated using several linear and non-linear examples.     

Kinetic friction for multi-material arbitrary Lagrangian Eulerian extended finite element formulations

An extended finite element method (X-FEM) for classical kinetic friction laws in a multi-material arbitrary Lagrangian Eulerian (MMALE) formulation is presented. The velocities of the nodes containing more than one material in their support are updated through the nodal accelerations to account for the kinetic friction effects. Numerical results are presented and discussed. Army Research Organization; contract/grant number: DAAD19-02-1-0266.     

An updated Lagrangian finite element sensitivity analysis of large deformations using quadrilateral elements

A continuum parameter and shape sensitivity analysis is presented for metal forming processes using the finite element method. The sensitivity problem is posed in a novel updated Lagrangian framework as suitable for very large deformations when remeshing operations are performed during the analysis. In addition to exploring the issue of transfer of variables between meshes for finite deformation analysis, the complex problem of transfer of design sensitivities (derivatives) between meshes for large deformation inelastic analyses is also discussed. A method is proposed that is shown to give accurate estimates of design sensitivities when remeshing operations are performed during the analysis. Sensitivity analysis for the consistent finite element treatment of near incompressibility within the context of the assumed strain methods is also proposed. In particular, the performance of four‐noded quadrilateral elements for the sensitivity analysis of large deformations is studied. The results of the continuum sensitivity analysis are validated by a comparison with those obtained by a finite difference approximation (i.e. using the solution of a perturbed deformation problem). The effectiveness of the method is demonstrated by applications in the design optimization of metal forming processes. Copyright © 2001 John Wiley & Sons, Ltd.     

Applications of linear inverse finite element method in prediction of the optimum blank in sheet metal forming

A linear inverse finite element method has been developed and investigated to predict the optimum blank. To reduce the computation time, the part is unfolded properly on the flat sheet and treated as a 2D problem. This approach is employed primarily to design the optimum blank shape from the desired final shape with the linear formulations. The procedure is based on the minimization of energy for the unfolded elements. Two solution methods, Direct and Newton–Raphson methods have been examined for the solution of nodal displacements in the equilibrium equations. The convergence show high sensitivity to the initial guess for the strain path when assumed to be linear at the first step. Two applied examples are implemented to show the efficiency of this method. In S rail example, the thickness distributions have been compared with experimental analysis after obtaining the optimum blank with Linear IFEM. In circular cup example, the results have been compared with conventional forward incremental method. New calculation of the external forces vector has been displayed. In this calculation, both blank holder force (BHF) vector and in-plane force vector have been shown. Finally, in this approach good agreement was found between the forward incremental and Linear IFEM results.     

Adaptive 2D finite element simulation of metal forming processes

The development and integration of available current methods and the development of new methods for an adaptive finite element analysis of metal forming processes are presented. The analysis includes large-strain, elastic–plastic, and thermal effects. Many numerical methods such as mesh generation, simulation of the contact between the workpiece and tool and die, and optimization of the finite element mesh are integrated and incorporated. In addition, an algorithm is developed which can detect certain severely distorted elements where the area of integration is approaching zero. The advantage of correcting these regions of locally distorted elements is demonstrated. These numerical methods are implemented in a finite element program developed for simulating metal forming processes, with the emphasis on automating the analysis. Examples include an axisymmetric stress simulation of a coldheading process, a plane strain simulation of an extrusion process and a plane strain simulation of orthogonal metal cutting, all with noticeable thermal effects. The orthogonal cutting forces and feed forces calculated are compared with two sets of experimental data, with good agreement.     

GH4169集合器超塑成形有限元分析及预成形研究

为了成功超塑成形GH4169高温合金集合器并降低研制成本,采用有限元分析对GH4169合金集合器超塑成形过程进行了数值模拟,并采用拉深成形工艺对集合器超塑成形所需的预成形进行了研究.结果表明:超塑成形需筒形预成形件,且聚料工步是超塑成形出满足设计要求的零件所必需的一道工序;成功地拉深出集合器超塑成形预成形件;合金经预拉深成形后,在超塑成形温度(950℃)下保温30 min后仍是ASTM 10级以上的细晶组织,能够满足超塑成形所需的细晶组织的要求.     

Process optimal design in non‐isothermal,steady‐state metal forming by the finite element method

A new approach to process optimal design in non‐isothermal, steady‐state metal forming is presented. In this approach, the optimal design problem is formulated on the basis of the integrated thermo‐mechanical finite element process model so as to cover a wide class of the objective functions and to accept diverse process parameters as design variables, and a derivative‐based approach is adopted as a solution technique. The process model, the formulation for process optimal design, and the schemes for the evaluation of the design sensitivity, and an iterative procedure for design optimization are described in detail. The validity of the schemes for the evaluation of the design sensitivity is examined by performing a series of numerical tests. The capability of the proposed approach is demonstrated through applications to some selected process design problems. Copyright © 1999 John Wiley & Sons, Ltd.     

Comparison of finite element reliability methods

The spectral stochastic finite element method (SSFEM) aims at constructing a probabilistic representation of the response of a mechanical system, whose material properties are random fields. The response quantities, e.g. the nodal displacements, are represented by a polynomial series expansion in terms of standard normal random variables. This expansion is usually post-processed to obtain the second-order statistical moments of the response quantities. However, in the literature, the SSFEM has also been suggested as a method for reliability analysis. No careful examination of this potential has been made yet. In this paper, the SSFEM is considered in conjunction with the first-order reliability method (FORM) and with importance sampling for finite element reliability analysis. This approach is compared with the direct coupling of a FORM reliability code and a finite element code. The two procedures are applied to the reliability analysis of the settlement of a foundation lying on a randomly heterogeneous soil layer. The results are used to make a comprehensive comparison of the two methods in terms of their relative accuracies and efficiencies.     

A novel finite element formulation for frictionless contact problems

This article advocates a new methodology for the finite element solution of contact problems involving bodies that may undergo finite motions and deformations. The analysis is based on a decomposition of the two-body contact problem into two simultaneous sub-problems, and results naturally in geometrically unbiased discretization of the contacting surfaces. A proposed two-dimensional contact element is specifically designed to unconditionally allow for exact transmission of constant normal traction through interacting surfaces.