D. A. Shishkanov, M. V. Vetchinnikov, Yu. N. Deryugin

FSUE RFNC – VNIIEF (Sarov, Russia)

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.

Key Words: peridynamics, continuum mechanics, molecular dynamics, nonlocal interactions, mesh-free method, fracture model, bond stiffness function

For citation: D. A. Shishkanov, M. V. Vetchinnikov, Yu. N. Deryugin. Peridynamics method for problems solve of solids destruction. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 24:4(2022), 452–468. DOI: https://doi.org/10.15507/2079-6900.24.202204.452-468

Information about the authors:

Dmitry A. Shishkanov, research laboratory mathematician, Russian Federal Nuclear Center (22 Yunosti St., Sarov 607182, Russia), ORCID: https://orcid.org/0000-0002-3063-4798, dima.shishkanov.96@mail.ru

Maxim V. Vetchinnikov, Head of research laboratory, Russian Federal Nuclear Center (22 Yunosti St., Sarov 607182, Russia), ORCID: https://orcid.org/0000-0003-0321-1738 vetchinnikov_max@mail.ru

Yuriy N. Deryugin, Chief Researcher, Russian Federal Nuclear Center (22 Yunosti St., Sarov 607182, Russia), Dr.Sci. (Phys.-Math.), ORCID: https://orcid.org/0000-0002-3955-775X, dyn1947@yandex.ru