Derivation of dual horizon state-based peridynamics formulation based on euler-lagrange equation

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)
17 Downloads (Pure)


The numerical solution of peridynamics equations is usually done by using uniform spatial discretisation. Although implementation of uniform discretisation is straightforward, it can increase computational time significantly for certain problems. Instead, non-uniform discretisation can be utilised and different discretisation sizes can be used at different parts of the solution domain. Moreover, the peridynamic length scale parameter, horizon, can also vary throughout the solution domain. Such a scenario requires extra attention since conservation laws must be satisfied. To deal with these issues, dual-horizon peridynamics was introduced so that both non-uniform discretisation and variable horizon sizes can be utilised. In this study, dual-horizon peridynamics formulation is derived by using Euler–Lagrange equation for state-based peridynamics. Moreover, application of boundary conditions and determination of surface correction factors are also explained. Finally, the current formulation is verified by considering two benchmark problems including plate under tension and vibration of a plate.

Original languageEnglish
Pages (from-to)841-861
Number of pages21
JournalContinuum Mechanics and Thermodynamics
Issue number3
Early online date14 Aug 2020
Publication statusPublished - 31 May 2023


  • dual horizon
  • peridynamics
  • Euler-Lagrange equations
  • non-local
  • state-based


Dive into the research topics of 'Derivation of dual horizon state-based peridynamics formulation based on euler-lagrange equation'. Together they form a unique fingerprint.

Cite this