A constitutive framework for anisotropic sand including non-proportional loading

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On the stress-force-fabric relationship for granular materials (2013, background): “Material behavior to non-proportional loading, involving rotation of either material fabric or principal stresses, has attracted much research interest over the last few decades (Arthur et al., 1980; Towhata and Ishihara, 1985; Gutierrez et al., 1991; Yoshimine et al., 1998; Li and Dafalias, 2004; T”
A critical state sand plasticity model accounting for fabric evolution (2014, methodology): “[41] and Li & Dafalias [33], but such mechanisms will complicate the formulation and are not considered in this paper.”
ISA model: A constitutive model for soils with yield surface in the intergranular strain space (2015, background): “According to [48, 53], the evolution of the fabric (fabric changes) can be neglected for small and medium strain amplitudes (k " k< 0:02).”
Anisotropic UH model for soils based on a simple transformed stress method (2017, methodology): “The most direct method is to use the fabric tensor to modify the strength or stiffness parameters in the models to be variables with the loading direction [15-23].”
Sand Plasticity Model Accounting for Inherent Fabric Anisotropy (2004, background): “In a more recent paper, Li and Dafalias (2004) have addressed the issue of general loading condition for their aforementioned work of 2002.”