Quasi-static responses elastomers

The material behavior above-described refers to the quasi-static response. However, elastomers subjected to real world loading conditions possess fluid-like characteristics typical of a viscoelastic material. When loaded by means of a stepwise strain, they stress-relax, i.e., the reaction force resulting from the application of an initial peak falls to an asymptotic value, which is theoretically reached after an infinite time [69]. Moreover, if an external force is suddenly applied, creep is observed and the strain begins to change slowly towards a limiting value. 

The non linear viscoelasticity of various particles filled rubber is addressed in range of studies. It is found that the carbon black filled-elastomer exhibit quasi-static and dynamic response of nonlinearity. Hartmann reported a state of stress which is the superposition of a time independent, long-term, response (hyperelastic) and a time dependent, short-term, response in carbon black filled-rubber when loaded with time-dependent external forces. The short term stresses were larger than the long term hyperelastic ones. The authors had done a comparative study for the non linear viscoelastic models undergoing relaxation, creep and hysteresis tests [20-22]. For reproducible and accurate viscoelastic parameters an experimental procedure is developed using an ad hoc nonlinear optimization algorithm. 

The behavior of carbon black-filled rubber in relation to quasi-static and dynamic responses is examined in detail. In particular, the main feamres of the microstructure of the material and their influence on the macro-mechanical response are highlighted. The effects of strain, strain-rate and temperature on the constitutive response are discussed. Mullins and Pa5me effects, which are peculiar in the behavior of filled elastomers, are reviewed and new results are shown. 

The behavior of filled elastomers can be primarily described as hyperelastic under static or quasi-static loading dissipative effects are negligible. There have been numerous experimental studies addressing the response of rubber under quasi-static loading conditions, including uniaxial tension/compression, shear, equibiaxial tension [53-56]. 

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