Abstract

This study investigates the transition from linear to non-linear viscoelastic behavior in polymers and rubber compounds under cyclic sinusoidal shear deformation. By employing Fourier series decomposition, we define the generalized elastic modulus,G′₀(γ₀) and viscous modulus to capture critical aspects of the material's response. The generalized elastic modulus G′₀(γ₀)is further divided into two components: the first harmonic, representing linear elasticity, and a nonlinear modulus G′_NLderived from higher harmonic contributions. To quantify the degree of nonlinearity, we introduce the Nonlinearity Index (NLI), defined as the ratio of the non-linear modulus to the first harmonic elastic modulus G′_NLand G′, providing a precise metric for non-linear viscoelastic behavior. We demonstrate the high sensitivity and utility of NLI in distinguishing different polymer topologies, particularly to differentiate between linear and branched macrostructures. Furthermore, we explore the influence of silica loading in silica-filled tread s-SBR compounds, revealing the pronounced nonlinearity induced by filler content and the sensitivity of NLI in detecting filler-rubber interactions. The study also examines functionalized solution styrene-butadiene rubber (s-SBR) in silica-based tread formulations for high-performance tires, emphasizing the critical role of polymer-filler interactions in dynamic reinforcement. Our findings establish NLI as a robust analytical tool for characterizing viscoelastic properties, offering valuable insight into molecular architecture and rubber-filler interactions for functionalized s-SBR compound.