In our examples, the magnitude of the out-of-balance forces is a fraction of a percent of the applied forces, but it cannot be assumed to be a numerical round-off error. We focus our investigation on the lack of overall equilibrium in an approach to couple peridynamics and classical continuum mechanics recently proposed by the authors. This can be the case even if the coupling strategy satisfies the usual numerical tests involving rigid body motions as well as uniform and linear strain distributions. This paper presents an overlooked issue in this type of coupled computational methods: the lack of overall equilibrium. Finally, based on the information reviewed above, the future research directions of crack branching modelling are discussed.read more read lessĪbstract: Coupling peridynamics based computational tools with those using classical continuum mechanics can be very beneficial, because it can provide a means to generate a computational method that combines the efficiency of classical continuum mechanics with the capability to simulate crack propagation, typical of peridynamics.

Next, a number of numerical methods that have been used to simulate crack branching are reviewed in detail, including the finite element method (FEM), extended finite element method (XFEM), boundary element method (BEM), meshfree methods (MMs), peridynamics (PD) and discrete element method (DEM). Then, the crack models including discrete crack models and smeared crack models are discussed, highlighting their key features, advantages and limitations. The experimental observations are first summarized, followed by the physics of crack branching. This paper provides a state-of-the-art review of crack branching, including experimental observations, physics, fracture models and associated numerical methods. At present, the field of crack branching is still at an exploration stage, lacking a unified explanation of the underlying mechanisms and an effective method to predict crack branching in practical materials. Abstract: Crack branching has important theoretical and practical significance in many natural phenomena and practical engineering problems.

Meshfree method examples