Peridynamics method for problems solve of solids destruction

Abstract. The article investigates the method of peridynamics, which is an alternative approach to solving destruction problems based on integral equations. It is assumed that particles in a continuum interact with each other at a finite distance, as in molecular dynamics. Damage is part of the theory at the level of two-particle interactions, so damage finding and destruction occurs when solving the equation of motion. During this work, bondbased and state-based peridynamics models of destruction used in the Sandia Laboratory were described and implemented within the framework of the MoDyS molecular dynamics software package. In the bond-based model, the defining relationship is the bond stiffness function, which corrects the force of particle-particle interaction and imposes a restriction on the use of the Poisson’s ratio. The state-based model generalizes the bond-based approach and may be applied to materials with any Poisson’s ratio. The relationship of both models is ascertained. Calculation convergence is demonstrated on the example of a one-dimensional elasticity problem. The possibility of using the implemented models for fracture problems is also shown.