On the Modelling of Fracture Using Strong Discontinuities

Licentiatavhandling, 2005

The major concern of this work is the constitutive and numerical modelling of fracture, based on strong discontinuity formulations. More particularly, an extended finite element approach is used, where the total displacement is separated in two mutually independent 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 the Eshelby stress (or energy-momentum) tensor. The fracture process is described by a cohesive zone model of damage-plasticity type relating the material Mandel stress and the inverse discontinuity. Interestingly, by confining the cohesive zone model entirely to the crack tip, the material crack driving force emerges as a reaction force at the tip. Due to the properties of this force, with magnitude corresponding to the well established J -integral and direction corresponding to the direction of maximum energy release, it is used to formulate an additional fracture criterion of Griffith type. The inverse formulation is also compared to a formulation based on the direct discontinuity, producing similar results. Also the numerical handling and computational implementation is addressed, including aspects as the numerical integration and linearisation of proposed models, the explicit finite element formulation with corresponding discretized equations as well as the particular procedure for successive discontinuity introduction.