On the modelling of mixed-mode discrete fracture: Part I - Damage models

In this manuscript, mixed-mode fracture is studied. Conversely to previous plasticity based formulations, the purpose of this work is to derive discrete damage models to simulate the evolution of fracture under both normal and shear tractions. First, an energy based model is used. Next, deformation-based models are adopted, both with isotropic and non-isotropic damage evolution laws. Damage is usually considered as a deformation driven process. However, fracture criteria, such as crack initiation and crack evolution, are typically defined in the stress or traction space. This is why a new, more refined model is also introduced, in which damage evolution is traction-based. Several special cases are studied, such as: homotetic damage evolution, isotropic damage evolution and a general mixed-mode evolution law. Compressive tractions are also dealt with, namely under Mode-II fracture. In all cases, as a direct consequence of the damage approach, both the total/secant constitutive relation and the corresponding incremental/-tangent stiffness are derived. Some elementary numerical results are obtained and discussed. (C) 2017 Elsevier Ltd. All rights reserved.