Refined bond-based peridynamics for thermal diffusion

Xin Gu (Department of Engineering Mechanics, Hohai University, Nanjing, China)
Qing Zhang (Department of Engineering Mechanics, Hohai University, Nanjing, China)
Erdogan Madenci (Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, USA)

Engineering Computations

ISSN: 0264-4401

Publication date: 24 July 2019



This paper aims to review the existing bond-based peridynamic (PD) and state-based PD heat conduction models, and further propose a refined bond-based PD thermal conduction model by using the PD differential operator.


The general refined bond-based PD is established by replacing the local spatial derivatives in the classical heat conduction equations with their corresponding nonlocal integral forms obtained by the PD differential operator. This modeling approach is representative of the state-based PD models, whereas the resulting governing equations appear as the bond-based PD models.


The refined model can be reduced to the existing bond-based PD heat conduction models by specifying particular influence functions. Also, the refined model does not require any calibration procedure unlike the bond-based PD. A systematic explicit dynamic solver is introduced to validate 1 D, 2 D and 3 D heat conduction in domains with and without a crack subjected to a combination of Dirichlet, Neumann and convection boundary conditions. All of the PD predictions are in excellent agreement with the classical solutions and demonstrate the nonlocal feature and advantage of PD in dealing with heat conduction in discontinuous domains.


The existing PD heat conduction models are reviewed. A refined bond-based PD thermal conduction model by using PD differential operator is proposed and 3 D thermal conduction in intact or cracked structures is simulated.



Gu, X., Zhang, Q. and Madenci, E. (2019), "Refined bond-based peridynamics for thermal diffusion", Engineering Computations, Vol. ahead-of-print No. ahead-of-print.

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