Nonlocal modeling of bi-material and modulus graded plates using peridynamic differential operator

Mehmet Dorduncu, Akif Kutlu, Erdogan Madenci, Timon Rabczuk

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


This study presents the application of the peridynamic differential operator (PDDO) on modeling of bi-material plates with/without modulus graded regions. The PDDO converts the Navier’s equilibrium equations and boundary conditions from the differential form into the integral form. The mismatch of the stiffness along the interface of two distinct materials results in an increase in the strain and stress variations, leading to the onset of cracking at the free corners of the interface. The interfacial strains and stresses can be mitigated by inserting a modulus graded layer between two different materials. The material properties in the modulus graded region is achieved through the power-law distribution. The efficacy of the proposed approach is demonstrated by considering a bi-material square plate under tension. The PDDO displacement, strain, and stress predictions are compared with the reference solutions, and good correlations are achieved. The influence of a modulus graded region with/without a pre-existing crack located between dissimilar materials is investigated for different material variations. It is noted that the PDDO performs very well on the displacement, strain, and stress predictions even if the solution domain has geometrical or material discontinuities. Moreover, modulus graded regions offer some advantages over the sharp interfaces and alleviate the strain and stress concentrations along the interface of the dissimilar materials.

Original languageEnglish (US)
Pages (from-to)893-909
Number of pages17
JournalEngineering with Computers
Issue number1
StatePublished - Feb 2023


  • Functionally graded materials
  • Material interfaces
  • Peridynamic differential operator
  • Stress analysis

ASJC Scopus subject areas

  • Software
  • Modeling and Simulation
  • Engineering(all)
  • Computer Science Applications


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