A general and efficient multistart algorithm for the detection of loss of ellipticity in elastoplastic structures

Abstract

SummaryThe present paper proposes a new efficient and robust algorithm for evaluating the loss of ellipticity criterion. While commonly used in two‐dimensional models for thin metal sheet forming processes, it is rarely evaluated in three‐dimensional structures due to the computational cost. The proposed algorithm is based on a Newton‐Raphson scheme and a multisampling 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 finiteelement method problem. These results are then used to predict the failure of an experimentally tested torsion sample.