Crack propagation modeling in two-dimensional isotropic plate using bond-based peridynamic theory‏

Abstract

Many problems of solids mechanics involve discontinuities in the body geometry or displacement field. A common example of these problems is the presence of cracks in the body. Analysis and modeling of the crack growth in bodies and structures is one of the important issues for designing methods to prevent crack growth or stop it and prevent sudden failure, thus increasing the lifetime of structures. Extensive research has been conducted to model the crack growth and failure in bodies. Despite the suggestion of various analytical and numerical methods to predict the path of crack growth in bodies, there are still many problems in modeling the crack growth and failure in bodies with single points and discontinuities. In recent years, a new theory called peridynamic theory has been proposed to model and analyze such problems. The formulation framework of the peridynamic theory is based on integral equations. Also, single points, discontinuities, and damage in the body and their modeling are another type of deformation and part of the structural equations of this theory. So, peridynamic theory can be used directly, without the need for additional relations, to model crack growth in problems with single points and discontinuities. In the present study, the dynamic crack growth was modeled and the factors affecting crack growth and branching in bodies were investigated using the peridynamic theory in LAMMPS software. Then, the results of this study were validated with those of others. The comparison of the obtained results shows that the peridynamic theory is well able to model the crack growth in structures and bodies in different complex states, without the need for changing the criteria. Also, how the crack grows and branches in the body depends on the stress applied to the body and the number of initial pre-cracks and the location and arrangement of them in the body.