LOCALIZING GRADIENT DAMAGE MODELS FOR QUASI-BRITTLE FRACTURE – SIZE EFFECT AND SIMPLE NUMERICAL IMPLEMENTATION

Abstract

The size effect of a quasi-brittle fracture is associated with the size of fracture process zone relative to the structural characteristic length. In this thesis, the localizing gradient enhancement is adopted to avoid the spurious spreading of damage suffered from the conventional nonlocal enhancement. Considering the three-point bend test of concrete beams, it is demonstrated that the dissipation profiles obtained with the localizing gradient enhancement compare well with those of reference meso-scale lattice models. With the correct damage evolution process, the localizing gradient enhancement is shown to capture the size effect phenomenon accurately for a series of geometrically similar concrete beams, using only a single set of material parameters. Next, a simple implementation of the localizing gradient damage model is elaborated. By utilizing the in-built coupled thermo-mechanical elements in Abaqus, the user only needs to define the material constitutive laws, as well as the sensitivity terms with respect to the field variables. Post-processing of results can be done directly in Abaqus. The applicability and ease of implementation are demonstrated via several examples, including those that utilize the Abaqus features of element deletion, contact between surfaces, as well as the incorporation of cohesive elements.