A general and efficient multi‐start algorithm for the detection of loss of ellipticity in elastoplastic structures

Abstract : The present paper proposes a new efficient and robust algorithm for evaluating the loss of ellipticity criterion. While commonly used in 2D models for thin metal sheet forming processes, it is rarely evaluated in 3D structures due to the computational cost. The proposed algorithm is based on a Newton-Raphson scheme and a multi-sampling optimization method based on a discretization method of the half unit sphere. First the new process is compared to the existing methods in the literature and then it is applied to a structural problem, namely tubes in torsion. The evolution of the loss of ellipticity in these structures is analyzed leading to conclusions about the failure of the structure. Meanwhile, the stability of the discretized problem is analyzed in order to better understand the loss of regularity of the FEM problem. These results are then used to predict the failure of an experimentally tested torsion sample in [1].
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Submitted on : Saturday, November 9, 2019 - 11:54:09 AM
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Moubine Al Kotob, Christelle Combescure, Matthieu Mazière, Tonya Rose, Samuel Forest. A general and efficient multi‐start algorithm for the detection of loss of ellipticity in elastoplastic structures. International Journal for Numerical Methods in Engineering, Wiley, 2019, ⟨10.1002/nme.6247⟩. ⟨hal-02357003⟩

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