A finite strain viscoplastic constitutive model for rubber with reinforcing fillers

A three dimensional viscoplastic constitutive model for finite strains in a co-rotational explicit scheme is developed and implemented using finite elements that captures the amplitude dependency, commonly referred to as the Fletcher-Gent effect, and frequency dependency of rubber with reinforcing fillers. The multiplicative split of the deformation gradient is utilized and the plastic flow rule stems from an extension to finite strains of a boundary surface model with a vanishing elastic region. The storage and loss modulus for a 50 phr carbon black filled natural rubber are captured over a large range of strain amplitudes, 0.2−50% shear strain, and frequencies, 0.2−20 Hz. In addition, bimodal excitation is replicated accurately, even though this measurement data is not included when obtaining material parameters. This capability is essential when non-sinusoidal loading conditions are to be replicated. By separating the material and geometrical influence on the properties of a component, the design engineers have the capability to evaluate more concepts early in the design phase. This also reduces the need of complex prototypes for physical testing, thereby saving both time and money.