@Article{icces.2023.09937,
AUTHOR = {Xingyu Kan, Yiwei Wang, Jiale Yan, Renfang Huang},
TITLE = {The Comparisons Between Peridynamic Differential Operators and  Nonlocal Differential Operators},
JOURNAL = {The International Conference on Computational \& Experimental Engineering and Sciences},
VOLUME = {25},
YEAR = {2023},
NUMBER = {2},
PAGES = {1--2},
URL = {http://www.techscience.com/icces/v25n2/53829},
ISSN = {1933-2815},
ABSTRACT = {Nonlocal differential operators have become an increasingly important tool in the field of numerical 
modeling and computational science. In recent years, two specific types of nonlocal differential operators 
have emerged as particularly useful in simulations of material and structural failures, such as fracture and 
crack propagations in solids. In this paper, the first type of nonlocal operator is based on the nonlocal 
operator theory in peridynamic theory, which is called PDOs [1,2]. The second type of nonlocal operator is 
derived from the Taylor series expansion of nonlocal interpolation, which is called NDOs [3-5]. NDOs are 
usually used to discretize the governing equations in the updated Lagrangian particle hydrodynamics 
(ULPH) method. While the differences of these two nonlocal operators may seem subtle, and they often 
cause confusion and misunderstandings. Therefore, this study is devoted to analyze and compare the 
differences between the two types of differential operators in terms of interpolation accuracy, crack 
expansion as well as multiphase flow simulation. It is found that, firstly, the NDOs are insensitive to the 
uniformity of particle distribution, and can converge in both uniform and non-uniform particle distributions, 
in contrast, PDOs can only yield convergent results in uniform particle distributions. Secondly, in the 
examples of crack propagation simulation, the results obtained by the PDOs have better agreement with 
experimental observations, and more suitable to handle the complex crack branching patterns. For 
simulating the rising bubble problem, NDOs can provide better results for the dynamic behaviors of rising 
bubble.},
DOI = {10.32604/icces.2023.09937}
}