The standard displacement-based FE formulation from solid mechanics has shown to be inadequate for the computation of quasi-brittle failure because of the spuriously mesh dependent results that it produces in terms of crack paths. The use of the mixed strain/displacement FE formulation has been proposed by the authors in the past to address this issue [1,2]. This approach guarantees the local convergence of the problem, allowing to obtain mesh objective results. In this presentation, the adoption of an Adaptive Formulation Refinement (AFR) scheme is proposed for the efficient analysis of structural failure. In this manner, the simulation can be initiated using the standard displacement-based FE formulation and the mixed FE is adaptively activated only in the regions where cracks develop. The standard formulation is maintained everywhere else in the domain during the calculation, enabling to introduce very significant savings in computational cost while taking advantage of the enhanced accuracy, local convergence and mesh objectivity provided when computing fracture with the mixed FE. The AFR strategy is used in combination with and Adaptive Mesh Refinement (AMR) scheme to further reduce the computational cost of the simulations. The adopted octree-based AMR approach allows to start the computation with an initially relatively coarse mesh and to adaptively refine it only in the regions where cracks develop. This enables the numerical evaluation of the quasi-brittle cracking phenomenon with sufficient accuracy while maintaining a reasonable cost of the simulations. An extensive set of benchmark problems and experiments have been analysed with the proposed framework, showing that it produces accurate structural responses, collapse mechanisms, crack trajectories and force-displacement curves. Computational efficiency is examined, demonstrating the ability to provide very significant savings in computational cost while producing mesh objective results.