On the mesh motion for ALE modeling of metal forming processes

The aim of this work is to develop a numerical framework for accurately and robustly simulating the different conditions exhibited by thermo-mechanical problems. In particular the work will focus on the analysis of problems involving large strains, rotations, multiple contacts, large boundary surface changes and thermal effects.The framework of the numerical scheme is based on the Particle Finite Element Method (PFEM) in which the spatial domain is continuously redefined by a distinct nodal reconnection, generated by a Delaunay triangulation. In contrast to classical PFEM calculations, in which the free boundary is obtained by a geometrical procedure (α−shape method), in this work the boundary is considered as a material surface, and the boundary nodes are removed or inserted by means of an error function.The description of the thermo-mechanical constitutive model is based on the concepts of large strains plasticity. The plastic flow condition is assumed nearly incompressible, so a u-p mixed formulation, with a stabilization of the pressure term via the Polynomial Pressure Projection (PPP), is proposed.One of the novelties of this work is the use of a combination between the isothermal split (Simo and Miehe [79]) and the so-called IMPL-EX hybrid integration technique (proposed by Oliver, Huespe and Cante [53]) to enhance the robustness and reduce the typical iteration number of the fully implicit NewtonRaphson solution algorithm. * Universitat Politècnica de Catalunya (UPC), Campus Terrassa, C/Colom 11, 08222 Terrassa, Spain.† International Center for Numerical Methods in Engineering (CIMNE), Campus Nord UPC, Gran Capitán, s/n., 08034 Barcelona, Spain. E-mail: cpuigbo@cimne.upc.edu.‡ Escola Tècnica Superior d'Enginyeries Industrial i Aeronàutica de Terrassa, Rambla de Sant Nebridi 22, 08222 Terrassa, Spain.§ International Center for Numerical Methods in Engineering (CIMNE), Campus Nord UPC, Gran Capitán, s/n., 08034 Barcelona, Spain. 2The new set of numerical tools implemented in the PFEM algorithm -including new discretization techniques, the use of a projection of the variables between meshes, and the insertion and removal of points-allows us to eliminate the negative Jacobians present during large deformation problems, which is one of the drawbacks in the simulation of coupled thermo-mechanical problems.Finally, two sets of numerical results in 2D are stated. In the first one, the behavior of the proposed locking free element type and different time integration schemes for thermo-mechanical problems is analyzed. The potential of the method for modeling more complex coupled problems as metal cutting and metal forming processes is explored in the last example.

Section: Endmentioning

confidence: 99%

The particle finite element method (PFEM) in thermo‐mechanical problems

Rodríguez

Carbonell

Cante

et al. 2016

“…Stress integration schemes like (22) require significant changes over existing schemes for small deformation and may lead to divergence or instability due to the use of the two stress measures. In the TL method by Bathe and Ozdemir [6], it is assumed that the Cauchy stresses in the constitutive laws can be directly replaced by the second Piola-Kirchhoff stresses so that the stress integration can be carried out as Equation (18). Such a scheme dramatically simplifies the integration, but will be shown to lead to inaccurate results in some cases.…”

Section: S T+ T Ijmentioning

confidence: 99%

“…Since the mesh motion is arbitrary in the ALE, there are several possibilities to find an optimum mesh and therefore different methods can be found in the literature, see e.g. References [14][15][16][17][18]. The most common method to determine the mesh motion is to remesh the domain by a mesh generation algorithm.…”

Section: Mesh Movementmentioning

confidence: 99%

See 1 more Smart Citation

Stress integration and mesh refinement for large deformation in geomechanics

Nazem

Sheng

Carter

2005

124

SUMMARYThis paper first discusses alternative stress integration schemes in numerical solutions to largedeformation problems in hardening materials. Three common numerical methods, i.e. the totalLagrangian (TL), the updated-Lagrangian (UL) and the arbitrary Lagrangian-Eulerian (ALE) methods, are discussed. The UL and the ALE methods are further complicated with three different stress integration schemes. The objectivity of these schemes is discussed. The ALE method presented in this paper is based on the operator-split technique where the analysis is carried out in two steps; an UL step followed by an Eulerian step. This paper also introduces a new method for mesh refinement in the ALE method. Using the known displacements at domain boundaries and material interfaces as prescribed displacements, the problem is re-analysed by assuming linear elasticity and the deformed mesh resulting from such an analysis is then used as the new mesh in the second step of the ALE method. It is shown that this repeated elastic analysis is actually more efficient than mesh generation and it can be used for general cases regardless of problem dimension and problem topology. The relative performance of the TL, UL and ALE methods is investigated through the analyses of some classic geotechnical problems.

“…Ghosh and Raju [19] proposed a nodal relocation technique that combines r-adaptation, which relocates nodes using a weighted average of node co-ordinates to minimize mesh distortion, with s-adaptation that employs hierarchical elements in zones of high gradient of plastic strain. In References [20][21][22] Gadala and Wang used the transfinite mapping to relocate mesh nodes. The ALE operator was separated in two steps: Lagrangian and Eulerian.…”

Section: Introductionmentioning

confidence: 99%

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

Aymone

2004

SUMMARYEfficient 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.