THE ENERGY OF ELASTIC DEFECTS - A DISTRIBUTIONAL APPROACH

An analysis of moving defects in homogeneous elastic materials is given in this paper. The laws of linear momentum, moment of momentum and energy are obtained in a distributional form. The motion of singularities gives rise to new terms in these balance laws. A quasistatic propagation criterion of energetic nature is used to obtain the balance of energy in the form of a conservation law for the material-defect system. The energy of this system consists of the elastic energy of the material and an additional term called the energy of the defect. It is uniformly distributed on the defect and its density represents, for two-dimensional bodies, the energy required to form a new unit defect area (or length). For cracks the existence of a Griffith-type surface energy distribution is obtained. For notches and cavities we show that an energy distributed over their boundary does not agree with the distributional form of the energy balance, which conduces to an energy distribution on the whole cavity. When the defect is an edge or screw dislocation, an energy distributed on the slip plane is obtained, its density being related to the Peach-Koehler force acting on the dislocation line.