## 1 Introduction  
Aluminum alloys are used extensively in a wide range of industries, including automobile, aerospace, transportation, and civilian infrastructure, with the material undergoing various processes such as rolling, extrusion, and forging to manufacture a component [1, 2, 3]. Depending upon the manufacturing operation, anisotropy can arise due to variations in as-manufactured material [4, 5, 6]. To predict the response of such materials, well-known isotropic yield functions based on the work of [PERSON] [7] and [PERSON] [8] have been modified by several researchers such as [PERSON] [9, 10, 11, 12], [PERSON] [13], [PERSON] [14], [PERSON] and [PERSON] [15], [PERSON] and [PERSON] [16], [PERSON] et al. [17, 18, 19, 20, 21], [PERSON] and [PERSON] [22], [PERSON] and [PERSON] [23], [PERSON] et al. [24], [PERSON] et al. [25] and [PERSON] and [PERSON] [26]. The widely used quadratic yield criterion of [PERSON] [9, 10] includes six material parameters that are obtained from uniaxial tensile and shear experiments for the three principal directions. Later, [PERSON] [11, 12] developed a modified version of the earlier formulation ([PERSON] [9, 10]) to model in-plane anisotropy for sheet metals. [PERSON] et al. [16, 17, 18, 19, 20] proposed different sets of anisotropic yield functions for metals, such as Yld91, Yld2000-2d, Yld 2004-8d, and Yld2004-18p. In particular, the Yld91 ([PERSON] [17]) criterion requires six parameters in the yield function formulation to model the material anisotropy. Later, [PERSON] [20, 21] ex tended this approach to linear transformation-based anisotropic yield functions, including Yld2004-8d and Yld2004-18p. [PERSON] et al. [27] performed numerical simulations and experiments to investigate the effect of plastic anisotropy on the mechanical behavior of a high-strength AA7075-T651 aluminum plate. In their work, the authors utilized the Yld2004-18p anisotropic yield function ([PERSON] [21]) to show that the experimentally observed anisotropic behavior of the plate could be modeled effectively. [PERSON] and [PERSON] [28] performed 3D finite element simulations using both anisotropic (Yld2004-3D) and isotropic ([PERSON], [8], and Hosford [13] models to predict the experimental material response of Al 6061-T6 sheet metal undergoing large strains. In their work, the anisotropy of the Al 6061-T6 sheet was characterized by a set of uniaxial and biaxial tests conducted in parallel using the 3D Yld2004-18P (Barlat [21]) yield criterion. The predicted material hardening behavior was assessed by comparing both measured and simulation-based force-displacement response, with results showing the Yld2004-18P model matches very well with the experimental result while the isotropic models have shown considerable deviation from the measurements. Additional relevant aluminum material investigations, including both experimental and numerical, can be found in the publications of [PERSON] and [PERSON] [29; 30; 31; 32], [PERSON] et al. [33], [PERSON] et al. [34], [PERSON] and [PERSON] [35], [PERSON] [36], [PERSON] et al. [37], [PERSON] et al. [38; 39], [PERSON] et al. [40], [PERSON] et al. [41], and [PERSON] [42], [PERSON] et al. [43] and their references. [PERSON] et al. [44] presented an approach based on incremental plasticity theory to determine the stresses and associated elastic and plastic strains from the total strain measured on a sample surface undergoing nominally plane stress or plane strain conditions. [PERSON] et al. [45] developed and applied the virtual fields method (VFM) to determine the constitutive parameters by calculating the stress fields from the heterogeneous strain fields, showing that the hardening law is important to predict the stress-strain relationship. More background on this subject can be found in [PERSON] et.al. [46], [PERSON] et al. [47], [PERSON] et al. [48], and [PERSON] & [PERSON] [49].