Failure modeling of quasi-brittle materials in terms of continuum damage mechanics model and finite element approach is presented in this paper. A stress-based implicit gradient-enhanced damage model using low-order finite elements is developed in which the characteristic length is a stress level dependent parameter. A simple formula for the calculation of the characteristic length of failure localization in the spatial discretization of materials is also taken, which is to additionally suppress the sensitivity of geometrical meshes. The displacements and nonlocal equivalent strain fields are approximated in the framework of low-order finite elements, i.e., the same interpolation functions are used for both primary variables. The spurious damaged zones and stress oscillation induced by the standard strain-based gradient damage can be overcome by using the proposed damage approach. Quasi-brittle materials such as concrete and limestone are considered and some numerical examples with different configuration are examined. The obtained numerical results are analyzed and are validated against reference solutions including experimental data and other existing numerical approaches
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