Nonlinear continuum dislocation theory revisited

•Definition of true resultant Burgers vector is given.•Thermodynamic framework of nonlinear CDT is proposed.•Governing equations of nonlinear CDT are derived.•Exact solution to the problem of finite antiplane constrained shear is found.•Dislocation density and stress–strain curve are computed.

The present paper provides the definition of resultant Burgers’ vector and the related dislocation density tensor in terms of the plastic deformation, regarded as that creating dislocations without deforming the crystal lattice. Based on this kinematics the thermodynamic framework of the finite strain continuum dislocation theory is developed. The proposed theory is then applied to the problem of antiplane constrained shear admitting an analytical solution.