A spectrum improved peridynamic model for shock wave problems

Abstract

Most previous peridynamics (PD) based shock wave modeling focuses on the field discontinuity problem but neglects the temporal discontinuous feature. Considering it is of vital importance to reproduce the shock jumps, the spectral properties of PD are studied and improved in this paper. A systematic theoretical analysis is firstly conducted and reveals the overly-dispersive behavior of PD model, including the oscillatory dispersion relation and zero energy modes. To suppress the consequent spurious oscillation, the dissipation effect is nonlocally introduced by viscosity as a minimum variation of conventional PD. Rather than applying the existing viscosities directly, the spectral balance is considered for the good control of both the oscillation and shock width, leading to the proposal of polynomial and force-limited viscous force states. The proposed model is then verified by several impact and explosion cases. The quantification of spectral balance is established and is employed for parameter calibration. The results suggest that the model shows good performance in shock wave modeling, with which both the suppression of oscillation and control of shock width near the shock jump are well achieved.