This paper formulated and implemented a novel local continuum damage model to be used with a continuous or a continuous-discontinuous strategy to simulate crack growth in quasi-brittle failure for mode I and mixed-mode conditions. The damage model is based on an evolution law using only physical parameters, which can be obtained through fracture and resistance tests without the need for further calibration. The local energy dissipation is controlled through regularization by the fracture energy and element length ensuring that different mesh densities dissipated the same energy during the damage evolution. The proposed damage model is employed in a finite element framework in two strategies: (i) a continuous strategy in which only the continuum damage model is used to predict crack propagation failure; and (ii) a continuous-discontinuous strategy in which a discontinuous enrichment is used to insert a crack within the elements after the total damage state is reached with no ad-hoc threshold value for the transition from continuous to the discontinuous approach. Comprehensive validation is demonstrated through comparisons with experimental results for various types of tests in mode I and mixed-mode conditions: single edge notch beam, unnotched four-point beam, anti-symmetric four-point shear beam, and double-edge-notched specimen. The results demonstrated that the proposed damage model and both strategies successfully simulated the crack propagation and failure of all simulated tests. Good agreement with the experimental results is observed for the crack path, maximum load, and entire load–displacement softening curves with coarser meshes than other models of the literature. Furthermore, the 3D results of the mixed-mode double-edge-notched specimen show that the proposed model provided good results even with coarser meshes using 16 times fewer elements than recent and similar results from the literature.