Mobility of lattice defects: discrete and continuum approaches

Abstract

In this paper, we study a highly idealized model of a moving lattice defect allowing for an explicit, “first principles” computation of a functional relation between the macroscopic configurational force and the velocity of the defect. The discrete model is purely conservative and contains information only about elasticities of the constitutive elements. The apparent dissipation is due to the presence of microinstabilities and the nonlinearity-induced tunneling of the energy from long to short wavelengths. This type of “radiative damping” is believed to be generic and accounting for a considerable fraction of inelastic irreversibility associated with fracture, plasticity and phase transitions. The paper contains direct comparison of the exact lattice solution with various continuum and quasicontinuum approximations. Despite its simplicity, the model can be used directly for the description of dynamic phase transitions in thin films.