The Green&apos;s functions for peridynamic non-local diffusion

doi:10.1098/rspa.2016.0185

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	The Green's functions for peridynamic non-local diffusion
	Wang, L. J. ; Xu, J. F. ; Wang, J. X.
刊名	PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
	2016
关键词	peridynamics non-local diffusion Green&apos heat conduction TRANSIENT HEAT-CONDUCTION COMPOSITE-MATERIALS TRANSPORT DISCONTINUITIES FORMULATION ELASTICITY DAMAGE MODEL s function
DOI	10.1098/rspa.2016.0185
英文摘要	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.; National Natural Science Foundation of China [11521202]; SCI(E); PubMed; ARTICLE; jxwang@pku.edu.cn; 2193; 20160185; 472
语种	英语
内容类型	期刊论文
源URL	[http://ir.pku.edu.cn/handle/20.500.11897/492693]
专题	工学院
推荐引用方式 GB/T 7714	Wang, L. J.,Xu, J. F.,Wang, J. X.. The Green's functions for peridynamic non-local diffusion[J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES,2016.
APA	Wang, L. J.,Xu, J. F.,&Wang, J. X..(2016).The Green's functions for peridynamic non-local diffusion.PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES.
MLA	Wang, L. J.,et al."The Green's functions for peridynamic non-local diffusion".PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES (2016).