A homogenized constitutive model for the anisotropic plastic deformation of perforated sheets H. Luo∗, X. Fan, M. Zhan Shaanxi Key Laboratory of High-Performance Precision Forming Technology and Equipment, Northwestern Polytechnical University, Xi’an 710072, China ∗ luohuan1169@mail.nwpu.edu.cn Keywords: Perforated sheets, Yield criterion, Anisotropic plastic deformation Perforated sheets show complex plastic deformation characteristics [1], because of the coupling of deformation characteristics between the matrix and the hole arrangement during plastic deformation. Modelling the macroscopic constitutive is important to providing a theoretical basis for the design of the forming process. Taking the commonly used perforated sheets with hexagonal arrays of circular holes as an example, the deformation characteristics are studied based on the unit cell model simulation under biaxial loading [2,3]. It can be found that the deformation is mainly concentrated in the connection area between the center of the holes. The stress is determined by two parts, which one is the component of the macroscopic stress on the corresponding section, and the other is the increased normal stress component caused by the additional bending moment. Therefore, a homogenized yield criterion which considering the effect of the additional bending moment is proposed. It can well describe the symmetry of the structure, as well as the equivalent performance of uniaxial, biaxial and tension-shear loading. Also, by constructing the parameters related to equivalent plastic strain and the associated flow rule, the anisotropic hardening and plastic flow of the perforated sheets can be quantified respectively. In addition, the proposed model shows good applicability in the square arrays of circular holes. References [1] Khatam, H., Pindera, M. J. (2011). Plastic deformation modes in perforated sheets and their relation to yield and limit surfaces. Int. J. Plast., 27, 1537-1559. [2] Xu, Z., Fan, X., Zhang, W., Wang, T. J. (2015). Numerical analysis of anisotropic elastoplastic deformation of porous materials with arbitrarily shaped pores. Int. J. Mech. Sci., 96, 121-131. [3] Takizawa, H., Furuta, S. (2023). Material modeling of perforated sheet metals with different hole arrangements by homogenization method. Mater. Trans., 64, 233-241. 82
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