Peridynamics contact model: Application to healing using phase field theory

Abstract

This paper presents a contact algorithm in non-ordinary state-based peridynamics (NOSB-PD) framework and its application in healing phase field (HPF) theory. The idea here is to exploit the nonlocality in PD to model the contact between two deformable bodies. The proposed method does not require artificial short-range force or additional degrees of freedom, e.g., Lagrange multiplier, which are often used in the conventional classical and PD contact models. In the regions where contact is likely to take place, neighbor search is performed at every time step and extra particles entering the horizon are identified. These extra particles form artificial bonds which transfer forces only in compression. This feature is essential for rebound simulation. Envisioning surface-to-surface bonding as the opposite process of cracking, we propose an HPF theory to model high velocity impact induced bonding between two material bodies. Here an HPF based bonding criterion is postulated and integrated with the proposed contact algorithm. The solution of the governing equations is obtained using the fourth order Runge-Kutta method. The efficacy of the proposed contact algorithm is demonstrated by simulations of impact and rebound of two plates, two cylinders, and cylinder with rectangular prism and comparing the energy time histories with finite element solutions obtained using ANSYS®. The potential of the proposed HPF theory is demonstrated through simulation of impact of two plates where the plates rebound when the impact velocity is below a critical value, and above that velocity, the plates join with each other.