Resumen de Meshfree methods applied to tensile fracture and compressive damagein quasibrittle materials
The interest of this current work was motivated by the difficulties encountered in studying the tensile and compressive failure observed in concrete beams with reinforcements. Employing cohesive models of fracture, we were able to reproduce the initiation and propagation of multiple cracks, for example the secondary cracks for beams without notch, local pull-out of the inclined reinforcement and the diagonal- tension failure. However the cumbersome computational effort involved prompted us to look for alternatives, which are not restricted by mesh distortion, artificial boundaries set for crack trajectories by the element interfaces. In pursuit of this objective, we take up the meshfree methods, in particular, those based on exponential shape functions.
Available meshfree methods can be classified in two categories according to the type of shape functions employed are of polynomial or exponential type. Consider its positive feature, the golden rule for shape functions, the exponential type appears to be a better alternative. For this reason, we choose to base our work on max-ent approximates. After carrying out detailed mathematical analysis, three important issues are addressed, these are imposing essential or Dirichlet boundary conditions, shape functions that are adaptive to the deformation field of each specific problem under study and insertion of a failure surface which may represent tensile fracture or compressive damage at the predicted location and direction
