Progress in mixed Eulerian‐Lagrangian finite element simulation of forming processes

Abstract

SUMMARYA review is given of a mixed Eulerian-Lagrangian finite element method for simulation of forming processes. This method permits incremental adaptation of nodal point locations independently from the actual material displacements. Hence numerical difficulties due to large element distortions, as may occur when the updated Lagrange method is applied, can be avoided. Movement of (free) surfaces can be taken into account by adapting nodal surface points in a way that they remain on the surface. Hardening and other deformation path dependent properties are determined by incremental treatment of convective terms. A local and a weighed global smoothing procedure is introduced in order to avoid numerical instabilities and numerical diffusion. Prediction of contact phenomena such as gap opening and/or closing and sliding with friction is accomplished by a special contact element. The method is demonstrated by simulations of an upsetting process and a wire drawing process.

Adaptive analysis of yield line patterns in plates with the arbitrary Lagrangian–Eulerian method

“…We have applied a split step algorithm [16,17] to solve Eq. (10). Firstly, the stresses and the state vari ables are updated at a material level, that is, no con vection is taken into account and the constitutive update is in fact fully Lagrangian.…”

“…Later, the extension towards nonlinear solids has been made [8]. In forming processes, the ALE method has proven successful [9,10]. More recently, the extension towards localisation analyses has been made [11,12].…”

On the design of lubricant free piston compressors

“…This method originates from fluid structure interaction analysis in the field of fluid dynamics. Later it was introduced for forming processes analysis to avoid mesh distortion when modeling large deformations [48] [47] [82] [83] and to simplify contact description [42] [81]. An ALE calculation step involves two additions with respect to an Updated Lagrangian step.…”

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

“…Several works about ALE formulation for 2D metal-forming processes can be found in literature [15][16][17][18][19][20][21][22][23][24].…”