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A mesh-free homotopic RPIM approach to simulate the two-dimensional material mixing during the FSW process

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Abstract

We propose in this work a high-order homotopic approach to simulate the material mixing during the FSW process. The technicality of the present approach is based on the coupling of RPIM, a temporal discretization, a homotopic transformation, a development in Taylor series and a continuation method. The formulation of the problem in strong form is based on the conservation equations of mass and momentum. The goal of this modeling is to minimize the number of inversions of the tangent matrices required by the iterative incremental methods. Indeed, a comparison of the results obtained via this algorithm will be made with those obtained by an iterative incremental method in order to verify the applicability of the proposed algorithm. The use of RPIM permits us to introduce exactly the boundary conditions around the tool of FSW process unlike the approximant meshless methods such as MLS.

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The data necessary to reproduce these results are obtained using an in-house code under Matlab. Interested researchers can contact the authors for any help.

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Authors and Affiliations

  1. Ecole Nationale des Sciences Appliquées, LISA Laboratory, Hassan First University of Settat, 26100, Berrechid, Morocco

    Said Mesmoudi & Omar Askour

  2. Laboratory of Materials, Signals, Systems and Physical Modeling, Department of Physics, Faculty of Sciences, University Ibn Zohr, Agadir, Morocco

    Mohammed Rammane

  3. Laboratory of Mechanical Engineering, Faculty of Science and Technology Fez, University Sidi Mohamed Ben Abdellah, Fez, Morocco

    Youssef Hilali & Oussama Bourihane

  4. Mathematics, Computer Science and Communication Systems Laboratory, National School of Applied Sciences of Safi, Cadi Ayyad University, Sidi Bouzid, BP 63, 46000, Safi, Morocco

    Omar Askour

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  1. Said Mesmoudi
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Mesmoudi, S., Rammane, M., Hilali, Y. et al. A mesh-free homotopic RPIM approach to simulate the two-dimensional material mixing during the FSW process. Arch Appl Mech 93, 3297–3311 (2023). https://doi.org/10.1007/s00419-023-02439-8

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