Numerical simulation of metal forming processes with 3D adaptive Remeshing strategy based on a posteriori error estimation

Abstract

In this work, a fully automated adaptive remeshing strategy, based on a tetrahedral element for 3D metal forming processes, was proposed in order to solve problems associated with the severe mesh distortion that occurs during the computation. The main idea is to use the h-type adaptive mesh in combination with an a-posteriori error estimator measured (by the energy norm) on each finite elements to locally control the mesh modification-as-needed. Once a new mesh is generated, all history-dependent variables must be carefully transferred between subsequent meshes. Therefore, several transfer techniques are described and compared. A special attention is given to restore the local mechanical equilibrium of the system with a new methodology. After presenting the necessary adaptive remeshing steps, some 3D analytic and numerical results using the proposed adaptive strategy are given to demonstrate the capabilities of the proposed equilibrated approach and to illustrate some practical characteristics of our remeshing process.

Sheet Metal Blanking Modeling Using Lode-Dependent Plasticity and Ductile Damage Models Combined with 3D Adaptive Remeshing Method

“…According to the large amount of plastic deformation undergone during sheet metal blanking, the initial mesh is highly distorted; frequent remeshing is needed during the computation in order to avoid mesh quality and also to control the errors caused by the approximation of the thermomechanical fields [49][50][51][52]. Two kinds of error estimates are proposed.…”

Thermomechanical coupling investigation in Ti-6Al-4V orthogonal cutting: Experimental and numerical confrontation

“…It is a direct consequence of the chosen numerical procedure and induces a lack of information in the primary shear zone as discussed above. Other than element deletion, the node splitting and the adaptative remeshing techniques present as powerful alternative to overcome the problem [68][69][70] . Indeed, a correction of this numerical artefact should be addressed in future works.…”

A simple history dependent remeshing technique to increase finite element model stability in elastic surface deformations

“…Excessive element distortion over a mesh, as shown in Figure 1c, introduces large, unacceptable error to the simulation, thereby jeopardising the accuracy of the model and possibly invalidating any further analysis. To overcome these complications and to continue the simulation, successive remeshing throughout the simulation is unavoidable [6].…”

“…Following the generation of a new mesh in the remeshing process, the simulation variables from the old degenerated mesh must be transferred to the new mesh. One can either completely recompute the simulation variables or transfer the variables from the old mesh to the new mesh [6]. If the optimal mesh configuration changes continuously thoughout the simulation (as is the case in the example shown in Figure 1) the second approach is generally considered preferable.…”

“…This process of transferring the history-dependent variables from the old to new mesh is known as historydependent remeshing. History-dependent remeshing techniques have been developed over the past 30 years prompted by the need for increasing model accuracy [6][7][8][9][10][11][12][13][14]. These transferal techniques can be broadly categorised into two groups; (1) techniques to transfer discontinuous variables which are continuous within each element and stored at Gauss points (referred to here as P 0 techniques) such as stress and strain (P 0 variables); and (2) techniques to transfer continuous variables stored at nodes (referred to here as P 1 techniques) such as displacement, velocity and temperate (P 1 variables) [9].…”