Mesh motion techniques for the ALE formulation in 3D large deformation problems

Efficient mesh motion techniques are a key issue to achieve satisfactory results in the arbitrary Lagrangian–Eulerian (ALE) finite element formulation when simulating large deformation problems such as metal‐forming. In the updated Lagrangian (UL) formulation, mesh and material movement are attached and an excessive mesh distortion usually appears. By uncoupling mesh movement from material movement, the ALE formulation can relocate the mesh to avoid distortion. To facilitate the calculation process, the ALE operator is split into two steps at each analysis time step: UL step (where deformation due to loading is calculated without convective terms) and Eulerian step (where mesh motion is applied). In this work, mesh motion is performed by new nodal relocation methods, developed for eight‐node hexahedral elements, which can move internal and boundary nodes, improving and concentrating the mesh in critical zones. After mesh motion, data is transferred from the UL mesh to the relocated mesh using an expansion of stresses in a Taylor's series. Two numerical applications are presented, comparing results of UL and ALE formulation with results found in the literature. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

An adaptive boundary-element approach to 3D transient free-surface flow of viscous fluids

An adaptive (Lagrangian) boundary-element approach is proposed for the general three-dimensional simulation of confined free-surface flow of viscous incompressible fluids. The method is stable as it includes remeshing capabilities of the deforming free surface, and thus can handle large deformations. A simple algorithm is developed for mesh refinement of the deforming free surface mesh. Smooth transition between large and small elements is achieved without significant degradation of the aspect ratio of the elements in the mesh. Several flow problems are presented to illustrate the utility of the approach.     

Interpolation with restrictions between finite element meshes for flow problems in an ALE setting

The need for remeshing when computing flow problems in domains suffering large deformations has motivated the implementation of a tool that allows the proper transmission of information between finite element meshes. Because the Lagrangian projection of results from one mesh to another is a dissipative method, a new conservative interpolation method has been developed. A series of constraints, such as the conservation of mass or energy, are applied to the interpolated arrays through Lagrange multipliers in an error minimization problem, so that the resulting array satisfies these physical properties while staying as close as possible to the original interpolated values in the L² norm. Unlike other conservative interpolation methods that require a considerable effort in mesh generation and modification, the proposed formulation is mesh independent and is only based on the physical properties of the field being interpolated. Moreover, the performed corrections are neither coupled with the main calculation nor with the interpolation itself, for which reason the computational cost is very low. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust adaptive remeshing strategy for large deformation,transient impact simulations

In this paper, an adaptive approach, with remeshing as essential ingredient, towards robust and efficient simulation techniques for fast transient, highly non‐linear processes including contact is discussed. The necessity for remeshing stems from two sources: the capability to deal with large deformations that might even require topological changes of the mesh and the desire for an error driven distribution of computational resources. The overall computational approach is sketched, the adaptive remeshing strategy is presented and the crucial aspect, the choice of suitable error indicator(s), is discussed in more detail. Several numerical examples demonstrate the performance of the approach. Copyright © 2005 John Wiley & Sons, Ltd.     

Numerical simulation of friction stir welding by natural element methods

In this work we address the problem of numerically simulating the Friction Stir Welding process. Due to the special characteristics of this welding method (i.e., high speed of the rotating pin, very large deformations, etc.) finite element methods (FEM) encounter several difficulties. While Lagrangian simulations suffer from mesh distortion, Eulerian or Arbitrary Lagrangian Eulerian (ALE) ones still have difficulties due to the treatment of convective terms, the treatment of the advancing pin, and many others. Meshless methods somewhat alleviate these problems, allowing for an updated Lagrangian framework in the simulation. Accuracy is not affected by mesh distortion (and hence the name meshless), but the price to pay is the computational cost, higher than in the FEM. The method used here, the Natural Element Method (NEM), presents some interesting characteristics, such as the ease of imposition of essential boundary conditions and coupling with FEM codes. Even more, since the method is formulated in a Lagrangian setting, it is possible to track the evolution of any material point during the process and also to simulate the Friction Stir Welding (FSW) of two slabs of different materials. The examples shown in this paper cover some of the difficulties related with the simulation of the FSW process: very large deformations, complex nonlinear and strongly coupled thermomechanical behaviour of the material and mixing of different materials.     

Automatic remeshing in 3‐D analysis of forming processes

Finite element modelling, employing updated Lagrangian techniques, is used extensively in the design and analysis of bulk forming processes. However, the full 3‐D capability has not seen widespread use in the automotive, aerospace, and, related industries due to, among other reasons, the need for remeshing, or, representation of the workpiece with a new finite element mesh as the analysis progresses. Automating the remeshing procedure of the deformed workpiece geometry would reduce the time required for a 3‐D analysis by several orders of magnitude. This paper discusses an algorithm for generating a new mesh to represent the deformed workpiece geometry during the analysis. The procedure is used to perform a 3‐D analysis of a valve forging problem. Copyright © 1999 John Wiley & Sons, Ltd.     

A contribution to error estimation and mapping algorithms for a hierarchical adaptive FE-strategy in finite elastoplasticity

The aim of this contribution is the presentation of an adaptive finite element procedure for the solution of geometrically and physically non-linear problems in structural mechanics. Within this context, the attention is mainly directed on the error estimation and hierarchical strategies for mesh refinement and coarsening in the case of finite elasto-plastic deformations. An important but sensitive aspect of adaptation approaches of the space discretization is the calculation of mechanical field variables for the modified mesh. Procedures of mesh refinement and coarsening imply the determination of strains, stresses and internal variables at the nodes and the Gauss points of new elements based on the transfer of the required data from the former mesh. In order to improve the efficiency as well as the convergence behaviour of the adaptive FE process an approach of data transfer primarily related to nodal values is presented. It is characterized by solving the initial value problem not only at the Gauss points but additionally at the nodes of the elements.     

Modeling of crack propagation via an automatic adaptive mesh refinement based on modified superconvergent patch recovery technique

In this paper, an automated adaptive remeshing procedure is presented for simulation of arbitrary shape crack growth in a 2D finite element mesh. The Zienkiewicz-Zhu error estimator is employed in conjunction with a modified SPR technique based on the recovery of gradients using analytical crack-tip fields in order to obtain more accurate estimation of errors. The optimization of crack-tip singular finite element size is achieved through the adaptive mesh strategy. Finally, several numerical examples are illustrated to demonstrate the effectiveness, robustness and accuracy of computational algorithm in calculation of fracture parameters and prediction of crack path pattern.     

Adaptive finite element remeshing in a large deformation analysis of metal powder forming

In this paper, a general framework for the finite element simulation of powder forming processes is presented. A large displacement formulation, based on a total and updated Lagrangian formulation and an adaptive finite element strategy based on error estimates and automatic remeshing techniques are utilized. To describe the constitutive model of the highly non‐linear behaviour of powder materials, an elliptical cap model based on a hardening rule to define the dependence of the yield surface on the degree of plastic straining is applied. The interfacial behaviour between the die and powder is modelled by using a plasticity theory of friction in the context of an interface element formulation. Finally, the powder behaviour during the compaction of a set of complex shapes are analysed numerically. The simulation of the deformation is shown as well as the distribution of relative density contours at different time stages. The results clearly indicate that the algorithm makes it possible to simulate the powder forming problems efficiently and automatically. Copyright © 1999 John Wiley & Sons, Ltd.     

An adaptive boundary‐element approach for 3D transient free surface cavity flow,as applied to polymer processing

An adaptive (Lagrangian) boundary‐element approach is proposed for the general three‐dimensional simulation of confined free surface flow of viscous incompressible fluids. The method is stable as it includes remeshing capabilities of the deforming free surface, and thus can handle large deformations. A simple algorithm is developed for mesh refinement of the deforming free surface mesh. Smooth transition between large and small elements is achieved without significant degradation of the aspect ratio of the elements in the mesh. Several flow problems are presented to illustrate the utility of the approach, particularly as encountered in polymer processing. These problems illustrate the transient nature of the flow in the extrusion through circular and square dies, the filling of circular and square disks as in conventional injection molding, and the flow during gas‐assisted injection molding inside a duct, with relevance to the important problem of viscous fingering. Copyright © 2001 John Wiley & Sons, Ltd.     

Remeshing strategies for large deformation problems with frictional contact and nearly incompressible materials

We present a framework to efficiently solve large deformation contact problems with nearly incompressible materials by implementing adaptive remeshing. Specifically, nodally integrated elements are employed to avoid mesh locking when linear triangular or tetrahedral elements are used to facilitate mesh re‐generation. Solution variables in the bulk and on contact surfaces are transferred between meshes such that accuracy is maintained and re‐equilibration on the new mesh is possible. In particular, the displacement transfer in the bulk is accomplished through a constrained least squares problem based on nodal integration, while the transfer of contact tractions relies on parallel transport. Finally, a residual‐based error indicator is chosen to drive adaptive mesh refinement. The proposed strategies are applicable to both two‐dimensional or three‐dimensional analysis and are demonstrated to be robust by a number of numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.     

On a consistent field transfer in non linear inelastic analysis and ultimate load computation

In this work we propose a field transfer operator for remeshing carried out in the course of incremental analysis of a non linear inelastic behavior. The proposed procedure is geared towards the ultimate load computation of a complex structure, where we choose the appropriate mesh grading for each different phase of computations, starting with a coarse mesh for the initial linear response and going towards a more refined mesh for highly nonlinear inelastic response. The proposed projection operator is developed on the basis of diffuse approximation method. The key feature of such an operator is to guarantee the conservation of relevant mechanics quantities which ensures a superior performance of the proposed field transfer with respect to the standard remeshing procedure. We present the illustrative results both for an isotropic damage model and standard plasticity model, indicating very satisfying performance.     

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.     

Adaptive superposition of finite element meshes in elastodynamic problems

An adaptive finite element procedure is developed for modelling transient phenomena in elastic solids, including both wave propagation and structural dynamics. Although both temporal and spatial adaptivity are addressed, the novel feature of the formulation is the use of mesh superposition to produce spatial refinement (referred to as s‐adaptivity) in transient problems. Spatial error estimation is based on superconvergent patch recovery of higher‐order accurate stresses and is used to guide mesh adaptivity, while the temporal error estimation is based on the assumption of linearly varying third‐order time derivatives of the displacement field and is used to adjust the time step size for the HHT‐α variant of the Newmark direct numerical integration method. Spatial adaptivity of the mesh is performed using a hierarchical h‐refinement scheme that is efficiently implemented using a structured version of finite element mesh superposition. This particular spatial adaptivity scheme is extremely fast and consequently makes it feasible to repeatedly update both the mesh and the time increment as required in an adaptive transient analysis. This work represents the initial effort in applying this type of spatial adaptivity to transient problems. Three example problems are given to demonstrate the performance characteristics of the s‐adaptive procedure. Copyright © 2005 John Wiley & Sons, Ltd.     

Explicit Reproducing Kernel Particle Methods for large deformation problems

The explicit Reproducing Kernel Particle Method (RKPM) is presented and applied to the simulations of large deformation problems. RKPM is a meshless method which does not need a mesh structure in its formulation. Because of this mesh-free property, RKPM is able to simulate large deformation problems without remeshing which is often required for the mesh-based methods such as the finite element method. The RKPM shape function and its derivatives are constructed by imposing the consistency conditions. An efficient treatment of essential boundary conditions is also proposed for explicit time integration. The Lagrangian method based on the reference configuration is employed for the RKPM simulation of large deformation problems. Several examples of non-linear elastic materials are solved to demonstrate the performance of the method. The numerical experiment for the problem of underwater bubble explosion is also performed using the explicit Lagrangian RKPM formulation. © 1998 John Wiley & Sons, Ltd.     

圆弧刃精密切削试验及其三维有限元分析

在商业化软件Marc的基础上建立了圆弧刃精密切削三维有限元模型,研究不同半径的圆弧刃精密切削条件下主切削力、切屑形状和切削温度场分布．该模型运用更新拉格朗日法的有限元方程、网格重划分准则,其刀一屑摩擦采用修正的库仑摩擦模型．模拟结果表明,圆弧刃的圆弧半径对主切削力、切屑形状和切屑的最高温度都有较大的影响．通过试验研究精密切削马氏体3J33在不同半径的圆弧刃条件下对主切削力的影响,结果表明模拟的主切削力与试验值在一定程度下是吻合的.