On the validity of peridynamic equation of motion in variable horizon domains

Nikpayam, J ; Sharif University of Technology | 2021

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  1. Type of Document: Article
  2. DOI: 10.1016/j.ijmecsci.2020.106245
  3. Publisher: Elsevier Ltd , 2021
  4. Abstract:
  5. Peridynamics is a nonlocal theory of solid mechanics which is suitable for modeling discontinuities and fractures without requiring external theories. In the original peridynamic equation of motion, the internal forces are integrated over the entire domain of the body. Although this equation complies perfectly with physical principles, its heavy calculations make it practically impossible to use. To avoid this difficulty, we can benefit from a special case of the peridynamic equation of motion in which the integration domain of the internal forces is limited to the family of particles. A limitation of this special equation, which is the most common equation in the peridynamic literature, is that it is only valid if the horizon is constant throughout the body. However, some of the peridynamic applications require that the horizon changes with position. In such cases, this common equation of motion imposes an additional force on particles. This force is the main source of artifacts known as ghost forces. In addition, this equation of motion cannot satisfy balance of linear momentum in a variable horizon domain. The root of these defects lies in limiting the integration domain of the internal forces to the family of particles. Such problems do not exist in the original peridynamic equation of motion. In this paper, an equation of motion based on the co-family of a particle is presented and compared with the existing equations. It is shown that the value of the original and the co-family internal force densities are equal, while the computational cost of the co-family internal force density is in the same order as the common internal force density, both are much less than the original one. It is also proved that the co-family equation of motion satisfies balance of linear momentum, whether the horizon is constant or variable. The provided analytical and numerical examples reveal a significant reduction in ghost forces using the co-family approach. © 2020 Elsevier Ltd
  6. Keywords:
  7. Computation theory ; Integration ; Additional forces ; Computational costs ; Equation of motion ; Internal forces ; Linear momenta ; Nonlocal theory ; Physical principles ; Solid mechanics ; Equations of motion
  8. Source: International Journal of Mechanical Sciences ; Volume 195 , 2021 ; 00207403 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0020740320343484