On the Modelling of Fracture Using Strong Discontinuities

The major concern of this work is the constitutive and numerical modelling of fracture,based on strong discontinuity formulations. More particularly, an extended finiteelement approach is used, where the total displacement is separated in two mutuallyindependent fields, representing the continuous and discontinuous displacement respectively.In this work, two different types of discontinuity representations are considered:one inverse (or material) and one direct (or spatial). Based on the inverse discontinuity,a general framework is derived within the concept of material forces, involving theEshelby stress (or energy-momentum) tensor. The fracture process is described by acohesive zone model of damage-plasticity type relating the material Mandel stress andthe inverse discontinuity. Interestingly, by confining the cohesive zone model entirelyto the crack tip, the material crack driving force emerges as a reaction force at thetip. Due to the properties of this force, with magnitude corresponding to the wellestablished J -integral and direction corresponding to the direction of maximum energyrelease, it is used to formulate an additional fracture criterion of Griffith type. Theinverse formulation is also compared to a formulation based on the direct discontinuity,producing similar results. Also the numerical handling and computational implementationis addressed, including aspects as the numerical integration and linearisation ofproposed models, the explicit finite element formulation with corresponding discretizedequations as well as the particular procedure for successive discontinuity introduction