Reduced strain gradient elasticity model with two characteristic lengths: fundamentals and application to straight dislocations

Abstract

In this paper, the reduced strain gradient elasticity model with two characteristic lengths is proposed and presented. The reduced strain gradient elasticity model is a particular case of Mindlin’s first strain gradient elasticity theory with a reduced number of material parameters and is a generalization of the simplified first strain gradient elasticity model to include two different characteristic length scale parameters. The two characteristic lengths have the physical meaning of longitudinal and transverse length scales. The reduced strain gradient elasticity model is used to study screw and edge dislocations and to derive analytical solutions of the dislocation fields. The displacement, elastic distortion, plastic distortion and Cauchy stress fields of screw and edge dislocations are non-singular, finite and smooth. The dislocation fields of a screw dislocation depend on one characteristic length, whereas the dislocation fields of an edge dislocation depend on up to two characteristic lengths. For the numerical analysis of the dislocation fields, the material parameters including the characteristic lengths have been used, computed from a second nearest neighbor modified embedded-atom method (2NN MEAM) potential for aluminum.