The following developments of such a constitutive approach have included cyclic loading conditions [12; 13] and an analysis of the healing phenomenon [14]. On the basis of the elastic-viscoelastic correspondence principle and continuum damage mechanics, the constitutive framework has been further elaborated to obtain a fatigue prediction model, which has also been compared to a classic phenomenological fatigue model [15; 16; 17]. It has been demonstrated that the regression coefficients of the phenomenological model can be expressed as functions of viscoelastic and damage characteristics of asphalt concretes. More recently, the modeling approach has been modified to consider the viscoplastic rate-dependent hardening-softening response of bituminous mixtures under compression [18; 19; 20; 21]. A viscoelastoplastic formulation of the constitutive approach has also been developed [22; 23]. Linear viscoelastic, rather than thermo-viscoplastic laws have also been studied by [PERSON] et al. [24; 25] to model the mechanical response of bituminous mixtures. A fundamental constitutive approach proposed by [PERSON] et al. [26] to model the permanent deformation of asphalt concretes at high temperatures was characterized by an anisotropic non-associated flow rule, on the basis of the Drucker-Prager yield surface. Laboratory data obtained by triaxial tests, carried out at different confining stress levels and strain rates, were used to validate the proposed model, with respect to three different asphalt concretes. Another relevant aspect of such an approach is the relationship that has been established between the model parameters and some significant aggregate properties (shape, surface energy, anisotropic distribution), particularly with regard to the optimization of the mixture. The research group of the Texas A & M University, after a series of studies [27; 28; 29; 30], achieved significant advances, leading up to a temperature-dependent viscodamage model coupled to the Schapery's nonlinear viscoelasticity and the Perzyna's viscoplasticity [31]. Such a model has allowed the ability to distinguish between the compressive and tensile response of asphalt concretes with respect to the damage development phenomenon. Advanced numerical algorithms were used to implement the proposed model in a general-purpose finite element code. An effective method to obtain the model parameters through the creep test carried out at various stress levels and temperatures was also developed. Further improvements have been accomplished over the years with more refined models based on the mechanics of materials [32; 33; 34; 35; 36; 37; 38; 39; 40] to acquire a deeper understanding about the complex relationship between asphalt mixtures' microstructure and their mechanical behavior. Particular emphasis has been given to the possibility of using such constitutive approaches to properly select asphalt concretes' components and their optimal proportions to ensure the required design properties and performance of the mixture. Furthermore, advanced material characterization methods have also been used to support such modeling approaches, for instance, techniques based on X-ray computed tomography image analysis. A coupled constitutive model, still based on Schapery nonlinear viscoelasticity and Perzyna-type viscoplasticity, but properly modified to take into account the hardening-relaxation phenomena, represents the current state of the art achieved by such a research group [41]. One of the key characteristics of the last approach is given by the possibility to calibrate and validate the model on the basis of conventional tests, namely dynamic modulus tests and repeated creep-recovery tests. The model has shown the capacity to properly describe the complex behavior of asphalt concretes under different loading conditions. Other studies, based on continuum thermomechanics, have allowed constitutive equations suitable for modelling the mechanical response of asphalt concretes to be obtained. [PERSON] et al.