Visco-elastic behavior through fractional calculus: an easier method for best fitting experimental results

In capturing visco-elastic behavior, experimental tests play a fundamental rule, since theyallow to build up theoretical constitutive laws very useful for simulating their own behavior.The main challenge is representing the visco-elastic materials through simple models,in order to spread their use. However, the wide used models for capturing both relaxationand creep tests are combinations of simple models as Maxwell and/or Kelvin, that dependon several parameters for fitting both creep and relaxation tests. This paper, following Nuttingand Gemant idea of fitting experimental data through a power law function, aims atstressing the validity of fractional model. In fact, as soon as relaxation test is well fittedby power law decay then the fractional constitutive law involving Caputo’s derivativedirectly appears. It will be shown that fractional model is proper for studying visco-elasticbehavior, since it may capture both relaxation and creep tests, requiring the identificationof two parameters only. This consideration is assessed by the good agreement betweenexperimental tests on creep and relaxation and the fractional model proposed. Experimentaltests, here reported are performed on two polymers having different chemical physicalproperties such that the fractional model may cover a wide range of visco-elastic behavior.