Non-ordinary State-based Peridynamics Free of Zero Energy Modes

Madenci E., Dördüncü M.

15th U.S. National Congress on Computational Mechanics (USNCCM15), Texas, United States Of America, 28 July - 01 August 2019

  • Publication Type: Conference Paper / Summary Text
  • City: Texas
  • Country: United States Of America
  • Erciyes University Affiliated: Yes


The non-ordinary state-based peridynamics (NOSB PD) is attractive because of its ability to employ existing constitutive relations for material models. The deformation gradient tensor and the force density vector appearing in the equilibrium equations are expressed in terms of nonlocal integrals. Their definitions affect the accuracy and stability of PD predictions and suffer from the presence of zero energy modes. Therefore, this study introduces a more accurate representation of the deformation gradient and the force density vector by using the concept of peridynamic differential operator (PDDO). Also, it presents both the weak and strong forms of NOSB PD simulations using implicit linear and nonlinear solvers. The numerical results demonstrate the numerical accuracy without numerical instability by considering a two-dimensional rectangular plate with and without a hole under quasi-static tension.