Numerical investigation of necking in perforated sheets using the periodic homogenization approach

Due to their attractive properties, perforated sheets are increasingly used in a number of industrial applications, such as automotive, architecture, pollution control, etc. Consequently, the accurate modeling of the mechanical behavior of this kind of sheets still remains a valuable goal to reach. This paper aims to contribute to this effort by developing reliable numerical tools capable of predicting the occurrence of necking in perforated sheets. These tools are based on the coupling between the periodic homogenization technique and three plastic instability criteria. The periodic homogenization technique is used to derive equivalent macroscopic mechanical behavior for a representative volume element of these sheets. On the other hand, the prediction of plastic instability is based on three necking criteria: the maximum force criterion (diffuse necking), the general bifurcation criterion (diffuse necking), and the loss of ellipticity criterion (localized necking). The predictions obtained by applying the three instability criteria are thoroughly analyzed and compared. A sensitivity study is also conducted to numerically investigate the influence on the prediction of necking of the design parameters (dimension, aspectratio, orientation, and shape of the holes), the macroscopic boundary conditions and the metal matrix material parameters (plastic anisotropy, hardening).