*Article* **Modeling the Full Time-Dependent Phenomenology of Filled Rubber for Use in Anti-Vibration Design**

### **Francesca Carleo 1, Jan Plagge 2, Roly Whear 3, James Busfield 1,\* and Manfred Klüppel 2**


Received: 16 March 2020; Accepted: 1 April 2020; Published: 6 April 2020

**Abstract:** Component design of rubber-based anti-vibration devices remains a challenge, since there is a lack of predictive models in the typical regimes encountered by anti-vibration devices that are deformed to medium dynamic strains (0.5 to 3.5) at medium strain rates (0.5/s to 10/s). An approach is proposed that demonstrates all non-linear viscoelastic effects such as hysteresis and cyclic stress softening. As it is based on a free-energy, it is fast and easily implementable. The fitting parameters behave meaningfully when changing the filler volume fraction. The model was implemented for use in the commercial finite element software ABAQUS. Examples of how to fit experimental data and simulations for a variety of carbon black filled natural rubber compounds are presented.

**Keywords:** viscoelastic behaviour; modelling; elastomer; cyclic softening
