Using a recent elasto-plastic theory of dislocation and disclination fields, a continuous representation of grain boundaries is introduced. Periodic arrays of wedge disclination dipoles, including those defined in the Disclination Structural Unit Model, are set-up as initial configurations in a dynamic model for symmetric tilt boundaries. These configurations are found to be unstable when the transport of disclinations is allowed. Driven by their self couple-stress field, the motion of disclinations leads to relaxation of the initial elastic curvature and stress fields and to nucleation and transport of relaxation dislocations, until an equilibrium configuration of lower energy is reached. Most of the residual elastic energy of grain boundaries is localized in a non-singular nanometric layer. This energy arises from alternative dilatation and contraction of the lattice around disclinations, and from lattice curvature and shear between disclination dipoles. By virtue of its continuous and dynamic character, the present theory allows modeling absolute misorientations and leads to energy density levels comparable to molecular statics findings.