Peridynamic bond-associated correspondence model: Wave dispersion property

The peridynamic bond-associated material correspondence model is a reformulation of the conventional correspondence model, in which the concept of bond-associated states were introduced to inherently remove the material instability. Numerical studies, in terms of deformation analysis, have shown the effectiveness of the bond-associated model in removing the material instability. In this study, the bond-associated model is further examined concerning its wave dispersion property. Detailed procedure to derive the wave dispersion relation in this model is outlined. Different combinations of the peridynamic material point horizon and the bond-associated horizon are studied for all three geometric dimensions. Potential effects of weight function on the wave dispersion property are also investigated. It is found that the bond-associated material correspondence model can effectively remove the material instability for practical applications. However, for all one-dimensional cases studied, except the conventional model, the initial slopes of all the wave dispersion curves are slightly larger than that predicted by the classical continuum mechanics model. For two-dimensional analysis, material instability still exists for the combination of the peridynamic material point horizon being twice of the mesh spacing and the bond-associated horizon being three times of mesh spacing. But compared to the conventional model, the material instability for this case was slightly improved as the intersections of the wave dispersion curve with the wavenumber axis were reduced from two to one. For the three representative weight functions studied, it is found that the weight function does not significantly change the wave dispersion relation in the bond-associated material correspondence model, except for the one-dimensional cases.