An efficient mode-of-deformation dependent rate-type constitutive relation for multi-modal cyclic loading of elastomers

We develop a 3D nonlinear viscoelastic model for filled elastomeric solids that exhibit good predictive capabilities across multiple deformation modes and strain rates using at most 11 parameters. Through the analysis-driven construction of the rate of dissipation within the rate -type thermodynamic framework of Rajagopal and Srinivasa (2000), we reduce the number of parameters and also introduce the mode-of-deformation-rate dependent viscosity (eta,,,(K3)) into the constitutive relations. The special form of eta,,,(K3) accounts for higher values of viscosity in tension as compared to that of other modes of deformation. The broad spectrum of relaxation times exhibited by the elastomers are characterized by categorizing it into short, medium, and long relaxations, each assumed to be associated with one of the three natural configurations. The strong mode-dependent response exhibited by HNBR50, where the compression-relaxation is faster than tension-relaxation, is predicted accurately only when all the natural configurations are active. In contrast, the response of NR is predicted by using just two natural configurations because the polymer molecules are restricted to two extremes of the relaxation spectrum as a consequence of the high affinity between carbon black and the polymer molecules. The entire model is implemented in Abaqus/Standard through the user subroutine UMAT that interacts with an external solver, DDASPK, which solves for the internal variables. We show that the analytical form for the consistent Jacobian can be derived, and establish the efficacy of the implementation by simulating non-homogeneous shear on a hockey puck geometry made of HNBR50 with a concave lateral surface. The simulation shows good agreement with experimental data.

Automated summary

We developed a 3D nonlinear viscoelastic model for filled elastomeric solids and achieved accurate predictions for multiple deformation modes and strain rates using a limited number of parameters. Through analysis, we reduced the parameters and introduced viscosity that depended on the mode of deformation rate into the constitutive relations. The model successfully captured the complex behavior of different elastomer materials, and the implementation in Abaqus/Standard yielded good agreement with experimental data.