Gradient elasticity theories in statics and dynamics a unification of approaches

Partly in response to a communication recently published in this journal on apparent inconsistencies between certain continuum and atomistic formulations of gradient elasticity (Yang and Guo 2005), we further elaborate on this issue in view of results and works not known or not cited in the aforementioned communication. In particular, we unify the concepts and motivations of two different formats of gradient elasticity. The first format was motivated for use in statics and aims at removing strain singularities. The second format was motivated for use in dynamics and aims at describing wave dispersion. We suggest here an alternative format of gradient elasticity that is dispersive, while its static version is identical to the first format mentioned above. Also, procedures are outlined by which the higher-order coefficients can be related to micro-structural properties. Finally, solution methods are described for static and dynamic analysis.