Multi-scale nonlinear modelling of sandwich structures using the Arlequin method |
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Authors: | Heng Hu Salim Belouettar Michel Potier-Ferry El Mostafa Daya Ahmed Makradi |
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Affiliation: | aSchool of Civil Engineering, Wuhan University, 8, South Road of East Lake, Wuchang, 430072 Wuhan, PR China;bCentre de Recherche Public Henri Tudor, 29, Avenue John F. Kennedy, L-1855 Luxembourg, G.D. of Luxembourg, Luxembourg;cLPMM, UMR CNRS 7554, I.S.G.M.P., Université Paul Verlaine-Metz, Ile du Saulcy, F-57045 Metz Cedex 01, France |
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Abstract: | The paper presents a combination of the Arlequin Method (AM) and the Asymptotic Numerical Method (ANM) for studying nonlinear problems related to the mechanical behavior of sandwich composite structures. The Arlequin Method is a multi-scale method in which different models are crossed and glued to each other. The ANM is an alternative method which falls into the category of numerical perturbation techniques. By introducing the power series expansions into the equilibrium equation, the nonlinear problem is transformed into a sequence of linear problems and solved by the standard finite element method. Compared to other classical solvers (Newton–Raphson Method, Modified Newton–Raphson Method), ANM offers a considerable interest in the computation time and reliability. To validate this method, the AM is combined with the ANM to simulate the local damage of 2D–2D and 2D–2D-coupled sandwich beams. The simulation results are compared to a reference solution calculated from a 2D beam without any coupling. In case of the 2D–2D-coupled sandwich beam, the simulation shows a good agreement with the reference solution for both the local damage and the deformation at the loaded point. However, in case of 2D–1D-coupled sandwich beam, the simulation deviate from the reference solution due to the constant thickness of the 1D zig-zag element used to model the 1D zone of the sandwich beam. |
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Keywords: | Arlequin ANM Multi-scale Nonlinear Sandwich |
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