A Possible Reason About Origin of Singularity and Anomalous Dispersion in Peridynamics

In the benchmark problems of peridynamics, there are some eccentric results, for example, singularity of uniaxial tension and anomalous dispersion of wave. The reasons to give rise to these results are investigated. We calculated local tension and wave of an infinite rod after adding a divergence of local stress in the peridynamic motion equation. The acquired results verify that the singularity in the peridynamic solution of local tension problem and anomalous dispersion of peridynamic wave are all eliminated. Therefore, the anomalous features of some peridynamic solutions likely stem from the lack of local stress characterizing contact interactions.