Peridynamic Modeling of Brittle Fracture in Mindlin-Reissner Shell Theory

In this work, we modeled the brittle fracture of shell structure in the framework of Peridynamics Mindlin-Reissener shell theory, in which the shell is described by material points in the mean-plane with its drilling rotation neglected in kinematic assumption. To improve the numerical accuracy, the stress-point method is utilized to eliminate the numerical instability induced by the zero-energy mode and rank-deficiency. The crack surface is represented explicitly by stress points, and a novel general crack criterion is proposed based on that. Instead of the critical stretch used in common peridynamic solid, it is convenient to describe the material failure by using the classic constitutive model in continuum mechanics. In this work, a concise crack simulation algorithm is also provided to describe the crack path and its development, in order to simulate the brittle fracture of the shell structure. Numerical examples are presented to validate and demonstrate our proposed model. Results reveal that our model has good accuracy and capability to represent crack propagation and branch spontaneously.

Automated summary

In this work, the brittle fracture of shell structure was modeled using the Peridynamics Mindlin-Reissener shell theory. The stress-point method was used to improve numerical accuracy and eliminate numerical instability. A novel crack criterion based on explicit representation of the crack surface by stress points was proposed. Instead of using the critical stretch, the classic constitutive model in continuum mechanics was used to describe material failure. A concise crack simulation algorithm was provided to describe crack path and development. Numerical examples validated the accuracy and capability of the proposed model in representing crack propagation and branching.