Generalized superposition rheology for characterizing anisotropic rheological properties of elastoviscoplastic materials

In this study, we propose an analytical framework to characterize rheological behavior under general superimposed flows, where steady shear is combined with oscillatory shear of arbitrary magnitude and orientation. Building upon the sequence of physical processes approach, the framework remains valid within flow conditions where the newly defined superposition number (Su) is less than or equal to 1. Its applicability was demonstrated through simulations of a model colloidal gel, a representative elastoviscoplastic material with complex rheological responses. The analysis captured rheological evolutions across a broad range of steady shear rates, offering interpretations closely connected to microstructural transitions—from the quiescent state to shear-induced densification and subsequently to rejuvenation and eventual fluidization. Distinct interference effects were observed in parallel superposition, where constructive and destructive interactions between steady and oscillatory shear produced two deltoids in the Cole–Cole plot. In contrast, orthogonal superposition, without such interference, resulted in a single deltoid. Overall, the proposed framework offers a powerful tool for superposition rheology, particularly for materials exhibiting complex structural and rheological transitions driven by flow-induced anisotropy.