Incompatible strain gradient elasticity of Mindlin type: screw and edge dislocations

Abstract The fundamental problem of dislocations in incompatible isotropic strain gradient elasticity theory Mindlin type, unsolved for more than half a century, is solved this work. Incompatible type the generalization Mindlin’s compatible including plastic fields providing way proper eigenstrain framework study defects like dislocations. Exact analytical solutions displacement fields, elastic distortions, Cauchy stresses, distortions and dislocation densities screw edge are derived. For numerical analysis constants have been used taken from ab initio DFT calculations. displacement, distortion, distortion stress non-singular, finite, smooth. depend on one characteristic length, whereas an up to three lengths. dislocation, obtained agree with corresponding ones simplified elasticity. In case depicted realistic Among others, looks physical core region good agreement computed atomistic simulations. Moreover, it shown that shape has asymmetric form due its inherent asymmetry possessing cylindrical symmetry It revealed considered incorporation lengths offers description only length.