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This work contributes to nonlocal vector calculus as an indispensable mathematical tool for the study of nonlocal models that arises in a variety of applications. We define the nonlocal half-ball gradient, divergence and curl operators with general kernel functions (integrable or fractional type with finite or infinite supports) and study the associated nonlocal vector identities. We study the nonlocal function space on bounded domains associated with zero Dirichlet boundary conditions and the half-ball gradient operator and show it is a separable Hilbert space with smooth functions dense in it. A major result is the nonlocal Poincaré inequality, based on which a few applications are discussed, and these include applications to nonlocal convection–diffusion, nonlocal correspondence model of linear elasticity and nonlocal Helmholtz decomposition on bounded domains.
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A nonconformal nonlocal approach to calculating statistical spread in fatigue indicator parameters for polycrystals
This articles intent is to convey that a weighted nonconformal nonlocal average is computationally tractable and has potential to predict a more accurate statistical spread in FIP values than other mesh independent nonlocal approaches considered.
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- Award ID(s):
- 1934753
- PAR ID:
- 10555601
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Fatigue & Fracture of Engineering Materials & Structures
- Volume:
- 46
- Issue:
- 12
- ISSN:
- 8756-758X
- Page Range / eLocation ID:
- 4801 to 4806
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1111/ffe.14158
