A thermodynamic framework for constitutive modeling of time- and rate-dependent materials. Part II: Numerical aspects and application to asphalt concrete

In this paper, we present within the finite element context the numerical algorithm for the integration of the thermodynamically consistent thermo-viscoelastic, thermo-viscoplastic, thermo-viscodamage, and thermo-healing constitutive equations derived in the first part of this paper. The nonlinear viscoelastic model is implemented using a recursive-iterative algorithm, whereas an extension of the classical rate-independent return mapping algorithm to the rate-dependent problems is used for numerical implementation of the viscoplasticity model. Moreover, the healing natural configuration along with the power transformation equivalence hypothesis, proposed in the first part of the paper, are used for the implementation of the viscodamage and micro-damage healing models. Hence, the thermo-viscoelastic and thermo-viscoplastic models are also implemented in the healing configuration. These numerical algorithms are implemented in the well-known finite element code Abaqus via the user material subroutine UMAT. A systematic procedure for identification of model parameters is presented. The model is then used to simulate the time-, temperature-, and rate-dependent response of asphalt concrete over an extensive set of experimental measurements including creep-recovery, creep, triaxial, constant strain rate, and repeated creep-recovery tests in both tension and compression. Comparisons of the model predictions and the experimental measurements show that the model is capable of predicting the nonlinear behavior of asphalt concrete subjected to different loading conditions.