Dislocations in Generalized Continuum Mechanics

An overview on dislocations in the framework of different types of generalized continua is given. We consider Cosserat elasticity, gradient Cosserat elasticity, strain gradient elasticity, and dislocation gauge theory. We review similarities and differences between these generalized continuum theories. In fact, we discuss the constitutive relations for the linear and isotropic case. Moreover, we demonstrate how the characteristic length scales are given in terms of the material parameters. Also, we discuss the mathematical solutions of the elastic fields of a screw dislocation.