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            <title xml:lang="en">ALE Formulation for the Numerical Simulation of Friction Stir Welding</title>
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              <p>An Arbitrary Lagrangian Eulerian approach is used to simulate the Friction Stir Process. This formulation, which has been implemented into the Forge3® FE software, uses a splitting method: 1) calculation of the material velocity/pressure fields, 2) calculation of the mesh velocity, and 3) treatment of advection terms. This latter stage consists in remapping the variables necessary to the next computation step. Transport of nodal variables is carried out relatively simply by using an upwind technique. However, remapping variables stored at integration points, as the stress field, require more complex operations. Different techniques, based on patch recovery approach, have been investigated.</p>
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