A new bond failure criterion for ordinary state-based peridynamic mode II fracture analysis

Peridynamics is a nonlocal theory, and it has been applied to a series of fracture problems based on its two main bond failure criteria: the critical stretch criterion and the critical energy density criterion. In this paper, a new criterion, the critical skew criterion, corresponding to the shear deformation, is for the first time proposed specifically for ordinary state-based peridynamic mode II fracture analysis. The necessity of the critical skew criterion is demonstrated by limitations and inaccuracy of the existing critical stretch and energy density criteria in theoretical and numerical mode II fracture analysis. The validity of the proposed critical skew criterion is illustrated by quantitative analysis of the captured behaviors of the typical mode II fracture tests. The results obtained by the critical skew criterion agree well with the benchmark data from the linear elastic theory, the virtual crack closure technique, and the Griffith's theory in different aspects of analysis. A simplified formula of the bond energy density is also derived and verified, and it can serves as a fundamental tool in peridynamic fracture analysis.