Deformation behavior of silica-filled rubber with coupling agents under monotonic and cyclic straining

•We provide new constitutive equation for gel phase.•We construct a unit cell model considering bunching structures of gel phase.•Formation of meniscus like gel phase provides essential physical enhancement mechanism of silica filled rubber.•Coupling agent markedly changes resistance to deformation and hysteresis loss.

A new constitutive equation for rubber is derived by employing a nonaffine molecular chain network model for elastic deformation behavior and the reptation theory for viscoelastic deformation behavior. The effect of a silica coupling agent, whose condensation reaction heterogeneously creates a crosslinking agent that increases the number of entangled points, on the deformation behavior is evaluated through the nonaffine constitutive equation for rubber. Precise TEM observation suggests the generation of complex interfillers connecting gel phases in which the characteristics of rubber intricately changed depending on the volume fraction of the silica coupling agent. The deformation behaviors of 2D rubber unit cells containing silica fillers under monotonic and cyclic strainings are investigated by computational simulation based on the proposed constitutive equation and the homogenization method. The obtained results clarified the essential physical enhancement mechanisms of deformation resistance and hysteresis loss, i.e., the Mullins effect, for silica-filled rubber. The volume fraction of the silica coupling agent essentially affects the deformation behavior of silica-filled rubber, the finding suggests that the material characteristics of silica-filled rubber are much more controllable than those of carbon-black-filled rubber.

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