A Non-ordinary State-based Godunov-peridynamics Formulation for Strong Shocks in Solids
The theory and meshfree implementation of peridynamics has been proposed to model problems involving transient strong discontinuities such as dynamic fracture and fragment-impact problems. For effective application of numerical methods to these events, essential shock physics and Gibbs instability should be addressed. The Godunov scheme for shock treatment has been shown an effective approach for tackling these two issues but has not been considered yet for peri-dynamics. This work introduces a physics-based shock modeling formulation for non-ordinary state-based peridynamics, in which the Godunov scheme is introduced by embedding the Rie-mann solution into the force state, resulting in a shock formulation free of tuneable parameters. Several benchmark problems are solved to demonstrate the effectiveness of the proposed formulation for modeling problems involving shocks in solids.