Peridynamic contact models for fracture analysis based on the micro-beam bond

Abstract

Contact problems are ubiquitous in engineering systems. Establishing contact models to predict the crack propagation and fracture is significant. Therefore, the present study proposes two peridynamic contact models for two-dimensional (2D) and three-dimensional (3D) contact problems based on the micro-beam bond and the Hertz theory, using the relative position of particles and the contact micromoduli to calculate the contact forces. Firstly, the strain is generated on the contact surface when two bodies come into contact. Simultaneously, the contact stiffness is obtained by the Hertz theory, and the contact forces are calculated according to the relationship between the strain of contact surface and the contact stiffness. Next, based on the peridynamic theory, the contact horizon and contact micromoduli are defined for the calculation of contact forces. Finally, the contact micromoduli for 2D and 3D contact problems are derived by equating the contact forces obtained from both theories. Additionally, this study defines the correction coefficients to reduce the calculation error of the proposed models and investigates the influence of different contact horizons on the calculation of contact forces. To validate the effectiveness of the proposed contact models, three numerical examples are compared with the results from the finite element method or experiments. It is demonstrated that the proposed contact models accurately calculate the contact forces and predict the crack propagation.