Dislocations in nonlocal simplified strain gradient elasticity: Eringen meets Aifantis
Markus Lazar
Abstract
The nonlocal strain gradient elasticity theory is used to address mechanical problems at small scales where size effects and regularization cannot be neglected. In this work, dislocations are investigated in the framework of nonlocal simplified first strain gradient elasticity. It is shown that nonlocal simplified strain gradient elasticity is the unification of the theories of Eringen’s nonlocal elasticity of Helmholtz type and simplified first strain gradient elasticity. Nonlocal simplified strain gradient elasticity contains two characteristic lengths, namely the characteristic length of nonlocal elasticity of Helmholtz type and the characteristic length of simplified first strain gradient elasticity. The advantage of nonlocal simplified first strain gradient elasticity is that the displacement, elastic distortion, plastic distortion, total stress, Cauchy stress and double stress fields of screw and edge dislocations which are calculated here are nonsingular and finite everywhere. Moreover, the Peach-Koehler force of two screw dislocations and two edge dislocations is derived and it is shown that the Peach-Koehler force is also nonsingular. Numerical examples for all dislocation fields of screw and edge dislocations in aluminum are given.