Recent advances in computational mechanics have opened the potential of carrying out the analysis and design of concrete structures in a realistic manner with the use of nonlinear concrete models. This encourages the development of more capable and realistic constitutive models, based on a rigorous approach, for the analysis and design of concrete structures. This research focuses on the development of a thermodynamic approach to constitutive modelling of concrete, with emphasis on the rigour and consistency both in the formulation of constitutive models, and in the identification of model parameters based on experimental tests. The key feature of the thermodynamic framework used in this study is that all behaviour of the defined model can be derived from two specified energy potentials. In addition, the derivation of a constitutive model within this framework merely follows procedures established beforehand. The proposed constitutive model here is based on continuum damage mechanics, in combination with plasticity theory, hence enabling the macroscopic material behaviour observed in experiments to be appropriately modelled. Damage-induced softening is the cause of many problems in numerical failure simulations based on conventional continuum mechanics. The resolution of these problems requires an appropriate special treatment for the constitutive modelling which, in this study, is based on nonlocal theory, and realized through the nonlocality of energy terms in the damage loading functions. For practical applications in structural analysis, the model requires a minimum number of parameters, which can be identified from experimental tests. All the above features of the model have been incorporated in a unified and consistent thermodynamic approach, which also distinguish the approach from existing ones. Numerical implementation and application are important parts of the study. A suitable implicit scheme is adapted here for the integration of the nonlocal rate constitutive equations. For the solution of systems of nonlinear algebraic equations in finite element analysis, the arc-length method in combination with local constraint equations employing dominant displacements is implemented, and proves its reliability in this study. Application of the proposed constitutive models in the analysis and design of concrete structures is straightforward, with several numerical examples showing the practical aspects of the proposed modelling.