Modeling the Payne effect in filled rubbers: accounting for time effect and partial reversibility

Abstract Carbon black-filled rubbers have been used in the industry since the early 20th century, and their mechanical advantages are well known. However, describing and predicting their mechanical behavior can become a non-trivial task. In this work, we present an approach to a new mechanical model that is capable of capturing the principal nonlinearities in rubber behavior when subjected to dynamic loadings, focusing on the Payne effect. Inspired by phase-change mechanisms, we introduce internal scalar variables to account for the carbon filler network dynamics in the presence of dynamic stretch. Reversibility of the Payne effect is taken into account within a clear and standard thermodynamical framework. This approach aims to enhance our understanding of the mechanical responses of carbon-filled rubbers and improve predictive capabilities.