STUDY OF WAVE DISPERSION AND PROPAGATION IN PERIDYNAMICS

Periydnamics (PD) is a new nonlocal method reformulated from solid mechanics. It adopts the integral form of governing equation and is naturally suitable to model fragments and cracks under extreme events, thus widely applied in the field of national defense security. However, the nonlocality in PD introduces the dispersion effect and imposes adverse effect on wave propagation, which will greatly restrict its capability in capturing solid behaviors, especially the fractures. For this purpose, we employ the spectral analysis method to study the dispersion behavior of PD system comprehensively. It is found that compared to the low frequencies, the dispersion relation of high frequency components shows an oscillation trend and zero-energy modes, leading to more serious dispersion problems. The dispersion behavior of high frequencies changes with the wave propagation direction and shows 45° symmetry in the spatial wave propagation. As the PD system itself is non-dissipative, the adverse effect of the dispersion problem can not be suppressed. As a result, the simulation accuracy may be greatly influenced. To introduce the numerical dissipation for dispersion effect suppression, the governing equation of viscosity introduction is proposed as a minimum variation of conventional PD. Both the typical deformation in solids and the selective suppression on high frequencies are considered then the corresponding viscous force state is constructed. Finally, a numerical study is conducted to model the shock waves under extreme events and investigate the influence of wave discontinuity. It is indicated that the wave discontinuity aggravates the dispersion problem and shows Gibbs instability in the wave propagation. These can be effectively suppressed by the viscous force state, which verifies the proposed method. This provides an important reference to reproduce the correct wave propagation process and obtain the reasonable solid behavior in PD, thus helps to support and guide the research of national defense security field.