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Finite Curved Creases in Infinite Is...

Mowitz, Aaron Jeremy.

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Finite Curved Creases in Infinite Isometric Sheets.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Finite Curved Creases in Infinite Isometric Sheets./
Author:	Mowitz, Aaron Jeremy.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2020,
Description:	56 p.
Notes:	Source: Dissertations Abstracts International, Volume: 82-07, Section: B.
Contained By:	Dissertations Abstracts International82-07B.
Subject:	Physics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28153764
ISBN:	9798557023429

Finite Curved Creases in Infinite Isometric Sheets.
Mowitz, Aaron Jeremy.

Finite Curved Creases in Infinite Isometric Sheets. - Ann Arbor : ProQuest Dissertations & Theses, 2020 - 56 p.

Source: Dissertations Abstracts International, Volume: 82-07, Section: B.

Thesis (Ph.D.)--The University of Chicago, 2020.

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

Geometric stress focusing, e.g. in a crumpled sheet, creates point-like vertices that terminate in a characteristic local crescent shape. The observed scaling of the size of this crescent is an open question in the stress focusing of elastic thin sheets. According to experiments and simulations, this size depends on the outer dimension of the sheet, but intuition and rudimentary energy balance indicate it should only depend on the sheet thickness. We address this discrepancy by modeling the observed crescent with a more geometric approach, where we treat the crescent as a curved crease in an isometric sheet. Although curved creases have already been studied extensively, the crescent in a crumpled sheet has its own unique features: the material crescent terminates within the material, and the material extent is much larger than the extent of the crescent. These features together with the general constraints of isometry lead to constraints linking the surface profile to the crease-line geometry. We construct several examples obeying these constraints, showing finite curved creases are fully realizable. This approach has some particular advantages over previous analyses, as we are able to describe the entire material without having to resort to excluding the region around the sharp crescent. Finally, we deduce testable relations between the crease and the surrounding sheet, and discuss some of the implications of our approach with regards to the scaling of the crescent size.

ISBN: 9798557023429Subjects--Topical Terms:

516296
Physics.
Subjects--Index Terms:

Elasticity

Finite Curved Creases in Infinite Isometric Sheets.
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100 1 $a Mowitz, Aaron Jeremy. $3 3554107
245 1 0 $a Finite Curved Creases in Infinite Isometric Sheets.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2020
300 $a 56 p.
500 $a Source: Dissertations Abstracts International, Volume: 82-07, Section: B.
500 $a Advisor: Witten, Thomas A.
502 $a Thesis (Ph.D.)--The University of Chicago, 2020.
506 $a This item must not be sold to any third party vendors.
520 $a Geometric stress focusing, e.g. in a crumpled sheet, creates point-like vertices that terminate in a characteristic local crescent shape. The observed scaling of the size of this crescent is an open question in the stress focusing of elastic thin sheets. According to experiments and simulations, this size depends on the outer dimension of the sheet, but intuition and rudimentary energy balance indicate it should only depend on the sheet thickness. We address this discrepancy by modeling the observed crescent with a more geometric approach, where we treat the crescent as a curved crease in an isometric sheet. Although curved creases have already been studied extensively, the crescent in a crumpled sheet has its own unique features: the material crescent terminates within the material, and the material extent is much larger than the extent of the crescent. These features together with the general constraints of isometry lead to constraints linking the surface profile to the crease-line geometry. We construct several examples obeying these constraints, showing finite curved creases are fully realizable. This approach has some particular advantages over previous analyses, as we are able to describe the entire material without having to resort to excluding the region around the sharp crescent. Finally, we deduce testable relations between the crease and the surrounding sheet, and discuss some of the implications of our approach with regards to the scaling of the crescent size.
590 $a School code: 0330.
650 4 $a Physics. $3 516296
650 4 $a Condensed matter physics. $3 3173567
650 4 $a Materials science. $3 543314
650 4 $a Particle physics. $3 3433269
653 $a Elasticity
653 $a Solid mechanics
653 $a Stress focusing
653 $a Thin sheets
653 $a Geometric stress focusing
690 $a 0605
690 $a 0611
690 $a 0794
690 $a 0798
710 2 $a The University of Chicago. $b Physics. $3 2102881
773 0 $t Dissertations Abstracts International $g 82-07B.
790 $a 0330
791 $a Ph.D.
792 $a 2020
793 $a English
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28153764