異方性Gursonの降伏関数を用いた多孔平板の有限要素解析

概要

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During the plastic deformation, the influence of voids on macroscopic mechanical behaviors is an important consideration, because ductile fracture occurs through the growth and the coalescence of voids. However, in order to analyze the model with distributed voids by finite element method directory, a large number of elements and nodes are required. Mesoscopic model which describes the effect of such voids by internal state variables is needed. In this paper, perforated sheets with randomly distributed holes are regarded as a two-dimensional ideal model of real ductile materials containing voids. The increase in stress around holes was approximated by the net stress tensor which incorporates the damage tensor obtained by the voronoi tessellation and the shape of each hole. Substituting the net stress into Gurson's yield function, an anisotropic Gurson's yield function and its constitutive relation are derived. Moreover, in order to evaluate the proposed mesoscopic model, the comparison was made between the mesoscopic and the usual FE analyses of sheets with randomly distributed holes. As a result, it is found that the proposed mesoscopic model well describes the macroscopic deformation of perforated sheets. The influence of the element size is also examined.