ABSTRACT
Literature reveals that almost 35% of the annual fuel consumed by a heavy vehicle is utilized to overcome rolling resistance of tyres. This dissipated energy adds to the annual carbon footprint. Hence, the ability to accurately predict the dissipated energy of the tyre compound is extremely valuable for a modern eco-friendly tyre manufacturer. In addition, the life of a tyre is directly correlated to the energy dissipated. In this study a numerical method to implement a novel model to capture the non-linear viscoelastic response of compressible filled rubber, using the UMAT subroutine of Abaqus a commercial Finite Element (FE) package, has been proposed. Hence the energy dissipated by the tyre compound, along with volumetric deformations, subjected to field conditions can be determined. The implementation of a viscoelastic model based on the concept of evolving natural configurations (Rajagopal & Srinivasa 2000) and the corresponding information on the variables to be defined within the UMAT subroutine, are presented. An Updated-Lagrangian formulation is used to implement the constitutive model. Since the constitutive relations are rather complex, the exact description of the material Jacobian is foregone; instead the consistent Jacobian is approximated numerically. UMAT subroutine of the constitutive model has been implemented for 3-D continuum elements. The response obtained using the UMAT has been compared with that obtained from a single point implementation of the same model using semi-inverse technique in MATLAB, for standard finite deformation schemes.
