The novel method of representative crack elements, recently developed in the context of phase-field fracture, is adopted to the eigenfracture method. It is shown, that in contrast to previous eigenerosion formulations, the predicted crack deformations fulfil the constraint in the proof of Γ-convergence. Unphysical predictions for crack deformations of previous eigenerosion models are shown for two elastic applications and are compared to the results of the novel approach as well as those of a discrete crack and a phase-field fracture model.