Representative volume element calculations under constant stress triaxiality, Lode parameter, and shear ratio

Recent experiments showed that the Lode parameter, which distinguishes between axisymmetric and shear dominated stress states, has a profound effect on material ductility, especially at low stress triaxiality (Bao and Wierzbicki, 2004; Barsoum and Faleskog, 2007a). Consequently, the theoretical framework for void growth and coalescence is currently being revisited, which often involves performing representative volume element (RVE) calculations. The present study investigates an RVE composed of a cubic unit cell containing a spherical void at its center. The void cell is subjected to a triaxial stress state with Σ11/Σ22=ρ11,Σ33/Σ22=ρ33Σ11/Σ22=ρ11,Σ33/Σ22=ρ33, plus an additional shear stress component Σ12/Σ22=ρ12Σ12/Σ22=ρ12. In the coordinate axes aligned with the edges of the cubic void cell, xixi (i=1,2,3i=1,2,3), the non-dimensional stress ratios ρ11,ρ33ρ11,ρ33, and ρ12ρ12 can be fully characterized by 3 parameters: the stress triaxiality, T, Lode parameter, L, and shear ratio, S  . The aim of this paper is to provide an effective method to keep T,LT,L, and S   values constant in the entire course of the loading. The effectiveness of the proposed method is validated through several examples covering a wide range of T,LT,L, and S values; the calculations are performed by using the general purpose finite element software ABAQUS.