Forces on dislocations due to strain gradients: Theories and two-dimensional simulations

Dislocations are topological defects known to be crucial in the onset of plasticity and in many properties of crystals. Classical elasticity fails to fully explain their dynamics under extreme conditions of high gradients of strain and small scales, which can nowadays be scrutinized. Previous works have proposed a type of force acting on dislocations when they are in the presence of strain gradients, the so-called core force. Here we designed a two-dimensional atomistic simulation through which we confirm the existence of this force, probe its properties, and measure its coefficients. The results of our simulations agree with the assumption that the core energy is the origin for the core force, but the coefficients of this force cannot be predicted by the approaches previously proposed. We show that the measured coefficients can be used to obtain the core energy in some systems such as ours. This way of evaluating the core energy can be compared to other existing approaches. Moreover, we show that the core force implies the existence of nonreciprocal interactions between dislocations. We believe that a correct consideration of the core force can be considered in mechanical modeling and in some theories trying to explain strange phenomena in plasticity.