Phenomenological Modelling of the Material Behaviour of Carbon Black-Filled Rubber in Continuum Mechanics

摘要

This paper proposes modelling concepts to represent the Mullins effect,rate depen-dence and the Payne effect.As a fundamental concept,wesplitthe stress intothe sum of an equilibrium stress and a rate-dependent overstress.There are two dif-ferent approaches for representing the overstress:the first one is based on the multiplicative Splitting of the deformation gradientintoelasticandinelasticpartsand,secondly,there is the functional repre-sentation with convolution Integrals.In order to model the Mullins effect we in-troduce a damage variable depending on the maximum deformation reached in the process history.To model the Payne effect we introduce an intrinsic time variable which is a functional of deformation history,specify an evolution law driven by a fractional time rate of deformation and calculate analytical formulae for the sto-rageandlossmoduli.Finally.itisshownthat both the frequency and amplitude de-pendence are well represented.