Thermo‐elasto‐plastic finite element analysis of quasi‐state processes in Eulerian reference frames

Abstract

SUMMARYAn Eulerian ÿnite element formulation for quasi-state one way coupled thermo-elasto-plastic systems is presented. The formulation is suitable for modeling material processes such as welding and laser surfacing. In an Eulerian frame, the solution ÿeld of a quasi-state process becomes steady state for the heat transfer problem and static for the stress problem. A mixed small deformation displacement elastoplastic formulation is proposed. The formulation accounts for temperature dependent material properties and exhibits a robust convergence. Streamline upwind Petrov-Galerkin (SUPG) is used to remove spurious oscillations. Smoothing functions are introduced to relax the non-di erentiable evolution equations and allow for the use of gradient (sti ness) solution scheme via the Newton-Raphson method. A 3-dimensional simulation of a laser surfacing process is presented to exemplify the formulation. Results from the Eulerian formulation are in good agreement with results from the conventional Lagrangian formulation. However, the Eulerian formulation is approximately 15 times faster than the Lagrangian.

Thermo-mechanical analysis of Wire and Arc Additive Layer Manufacturing process on large multi-layer parts

“…For a long weld with a constant welding speed, the thermal histories approach a steady state, particularly in the middle of the weld. This phenomenon has been utilised in FE models of welding processes which have used a steady state model [13][14][15][16]18].…”

“…Moreover, the model using the Eulerian frame does not need to use a high density mesh uniformly along the weld line, saving additional computational time [14]. While the steady state solution of the thermal problem is relatively trivial, application to the mechanical problem is more difficult, but has been demonstrated by several authors [13,14,16,17]. An alternative approach, developed by Colegrove et al [18] cut the Eulerian thermal model into a series of temperature data slices, and then transferred the sliced temperature data onto a 2D elastic-plastic model.…”

Optimization of thermo‐elasto‐plastic processes using Eulerian sensitivity analysis

“…The expression for the derivative of the equivalent plastic strain component R q is obtained by di erentiating Equation (38).…”

“…The ÿnite element formulation for Eulerian heat transfer analysis is summarized thereafter [18,20,21]. The displacement based mixed Galerkin formulation for the elasto-plastic ÿnite element problem in an Eulerian frame is also presented [20,38].…”

“…Using the associative J 2 plasticity [39], the yield function f, and equivalent plastic strain q are In the above equations, the notation˙ denotes the time derivative @ =@t. For a quasi-static analysis, the time rate equations become incremental equations. Di erentiating Equations (18) and (19), and substituting in Equations (20) and (21), the plasticity evolution equations are derived as follows [38]:…”