title: The Green's functions for peridynamic non-local diffusion.
abstract: In this work, we develop the Green's function method for the solution of the peridynamic non-local diffusion model in which the spatial gradient of the generalized potential in the classical theory is replaced by an integral of a generalized response function in a horizon. We first show that the general solutions of the peridynamic non-local diffusion model can be expressed as functionals of the corresponding Green's functions for point sources, along with volume constraints for non-local diffusion. Then, we obtain the Green's functions by the Fourier transform method for unsteady and steady diffusions in infinite domains. We also demonstrate that the peridynamic non-local solutions converge to the classical differential solutions when the non-local length approaches zero. Finally, the peridynamic analytical solutions are applied to an infinite plate heated by a Gauss source, and the predicted variations of temperature are compared with the classical local solutions. The peridynamic non-local diffusion model predicts a lower rate of variation of the field quantities than that of the classical theory, which is consistent with experimental observations. The developed method is applicable to general diffusion-type problems.
authors.affiliation: State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science , College of Engineering, Peking University , Beijing 100871, People's Republic of China.
authors.forename: L J
authors.initials: LJ
authors.lastname: Wang
authors.affiliation: Beijing Aeronautical Science and Technology Research Institute , Beijing 100083, People's Republic of China.
authors.forename: J F
authors.initials: JF
authors.lastname: Xu
authors.affiliation: State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, People's Republic of China; CAPT, HEDPS and IFSA Collaborative Innovation Center of MoE, Peking University, Beijing 100871, People's Republic of China.
authors.forename: J X
authors.identifier: 0000-0003-0977-833X
authors.initials: JX
authors.lastname: Wang
keywords: Green’s function; heat conduction; non-local diffusion; peridynamics