Email this article Investigation of different influence functions in peridynamics
- Authors: Deryugin Y.N.1, Vetchinnikov M.V.2, Shishkanov D.A.1
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Affiliations:
- Russian Federal Nuclear Center National Research Mordovia State University
- Russian Federal Nuclear Center
- Issue: Vol 25, No 4 (2023)
- Pages: 342-360
- Section: Mathematical modeling and computer science
- Published: 24.11.2023
- URL: https://journals.rcsi.science/2079-6900/article/view/360900
- DOI: https://doi.org/10.15507/2079-6900.25.202304.342-360
- ID: 360900
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Abstract
Peridynamics is a non–local numerical method for solving fracture problems based on integral equations. It is assumed that particles in a continuum are endowed with volume and interact with each other at a finite distance, as in molecular dynamics. The influence function in peridynamic models is used to limit the force acting on a particle and to adjust the bond strength depending on the distance between the particles. It satisfies certain continuity conditions and describes the behavior of non-local interaction. The article investigates various types of influence function in peridynamic models on the example of three-dimensional problems of elasticity and fracture. In the course of the work done, the bond-based and state-based fracture models used in the Sandia Laboratory are described, 6 types of influence functions for the bond-based model and 2 types of functions for the state-based model are presented, and the corresponding formulas for calculating the stiffness of the bond are obtained. For testing, we used the problem of propagation of a spherically symmetric elastic wave, which has an analytical solution, and a qualitative problem of destruction of a brittle disk under the action of a spherical impactor. Graphs of radial displacement are given, raster images of simulation results are shown.
About the authors
Yuriy N. Deryugin
Russian Federal Nuclear CenterNational Research Mordovia State University
Email: dyn1947@yandex.ru
ORCID iD: 0000-0002-3955-775X
Chief Researcher
professor, Department of Applied Mathematics, Differential Equations and Theoretical Mechanics
Russian Federation, 22 Yunosti St., Sarov 607182, Russia 68/1 Bolshevistskaya St., Saransk 430005, RussiaMaxim V. Vetchinnikov
Russian Federal Nuclear Center
Email: vetchinnikov_max@mail.ru
ORCID iD: 0000-0003-0321-1738
Head of research laboratory
Russian Federation, 22 Yunosti St., Sarov 607182, RussiaDmitry A. Shishkanov
Russian Federal Nuclear CenterNational Research Mordovia State University
Author for correspondence.
Email: dima.shishkanov.96@mail.ru
ORCID iD: 0000-0002-3063-4798
research laboratory mathematician,
postgraduate, Department of Applied Mathematics, Differential Equations and Theoretical Mechanics
Russian Federation, 22 Yunosti St., Sarov 607182, Russia 68/1 Bolshevistskaya St., Saransk 430005, RussiaReferences
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