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Nonlocal Neumann Volume-Constrained ...

Tao, Yunzhe.

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Nonlocal Neumann Volume-Constrained Problems and Their Application to Local-Nonlocal Coupling.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Nonlocal Neumann Volume-Constrained Problems and Their Application to Local-Nonlocal Coupling./
Author:	Tao, Yunzhe.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
Description:	135 p.
Notes:	Source: Dissertations Abstracts International, Volume: 80-08, Section: B.
Contained By:	Dissertations Abstracts International80-08B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13428404
ISBN:	9780438883383

Nonlocal Neumann Volume-Constrained Problems and Their Application to Local-Nonlocal Coupling.
Tao, Yunzhe.

Nonlocal Neumann Volume-Constrained Problems and Their Application to Local-Nonlocal Coupling. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 135 p.

Source: Dissertations Abstracts International, Volume: 80-08, Section: B.

Thesis (Ph.D.)--Columbia University, 2019.

This item must not be sold to any third party vendors.

As alternatives to partial differential equations (PDEs), nonlocal continuum models given in integral forms avoid the explicit use of conventional spatial derivatives and allow solutions to exhibit desired singular behavior. As an application, peridynamic models are reformulations of classical continuum mechanics that allow a natural treatment of discontinuities by replacing spatial derivatives of stress tensor with integrals of force density functions. The thesis is concerned about the mathematical perspective of nonlocal modeling and local-nonlocal coupling for fracture mechanics both theoretically and numerically. To this end, the thesis studies nonlocal diffusion models associated with ``Neumann-type'' constraints (or ``traction conditions'' in mechanics), a nonlinear peridynamic model for fracture mechanics with bond-breaking rules, and a multi-scale model with local-nonlocal coupling. In the computational studies, it is of practical interest to develop robust numerical schemes not only for the numerical solution of nonlocal models, but also for the evaluation of suitably defined derivatives of solutions. This leads to a posteriori nonlocal stress analysis for structure mechanical models.

ISBN: 9780438883383Subjects--Topical Terms:

1669109
Applied Mathematics.
Subjects--Index Terms:

Local-nonlocal coupling

Nonlocal Neumann Volume-Constrained Problems and Their Application to Local-Nonlocal Coupling.
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245 1 0 $a Nonlocal Neumann Volume-Constrained Problems and Their Application to Local-Nonlocal Coupling.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2019
300 $a 135 p.
500 $a Source: Dissertations Abstracts International, Volume: 80-08, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Du, Qiang.
502 $a Thesis (Ph.D.)--Columbia University, 2019.
506 $a This item must not be sold to any third party vendors.
520 $a As alternatives to partial differential equations (PDEs), nonlocal continuum models given in integral forms avoid the explicit use of conventional spatial derivatives and allow solutions to exhibit desired singular behavior. As an application, peridynamic models are reformulations of classical continuum mechanics that allow a natural treatment of discontinuities by replacing spatial derivatives of stress tensor with integrals of force density functions. The thesis is concerned about the mathematical perspective of nonlocal modeling and local-nonlocal coupling for fracture mechanics both theoretically and numerically. To this end, the thesis studies nonlocal diffusion models associated with ``Neumann-type'' constraints (or ``traction conditions'' in mechanics), a nonlinear peridynamic model for fracture mechanics with bond-breaking rules, and a multi-scale model with local-nonlocal coupling. In the computational studies, it is of practical interest to develop robust numerical schemes not only for the numerical solution of nonlocal models, but also for the evaluation of suitably defined derivatives of solutions. This leads to a posteriori nonlocal stress analysis for structure mechanical models.
590 $a School code: 0054.
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Mathematics. $3 515831
653 $a Local-nonlocal coupling
653 $a Nonlocal Neumann volume-constrained problems
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710 2 $a Columbia University. $b Applied Mathematics. $3 3179529
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