THE ENERGY OF ELASTIC DEFECTS - A DISTRIBUTIONAL APPROACH

An analysis of moving defects in homogeneous elastic materials is give n in this paper. The laws of linear momentum, moment of momentum and e nergy are obtained in a distributional form. The motion of singulariti es gives rise to new terms in these balance laws. A quasistatic propag ation criterion of energetic nature is used to obtain the balance of e nergy in the form of a conservation law for the material-defect system . The energy of this system consists of the elastic energy of the mate rial and an additional term called the energy of the defect. It is uni formly distributed on the defect and its density represents, for two-d imensional bodies, the energy required to form a new unit defect area (or length). For cracks the existence of a Griffith-type surface energ y distribution is obtained. For notches and cavities we show that an e nergy distributed over their boundary does not agree with the distribu tional form of the energy balance, which conduces to an energy distrib ution on the whole cavity. When the defect is an edge or screw disloca tion, an energy distributed on the slip plane is obtained, its density being related to the Peach-Koehler force acting on the dislocation li ne.