Impact-induced wave patterns in a slender cylinder composed of a non-convex elastic material

Hui-Hui Dai; Zhenli Xu

Impact-induced wave patterns in a slender cylinder composed of a non-convex elastic material

Hui-Hui Dai^*
, Zhenli Xu

^*Corresponding author for this work

Department of Mathematics

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

Abstract

This paper studies nonlinear wave propagation in a slender elastic cylinder due to impacts. One purpose is to examine what kinds of wave patterns can arise when both the material nonlinearity caused by a non-convex energy function and the dispersion caused by the lateral movement are present. A high-order weighted essentially non-oscillatory (WENO) scheme is used to obtain the numerical solutions of a model equation which takes into account the dispersion and the above-mentioned nonlinearity. It turns out that a variety of wave patterns can appear, including the co-existence of a transformation front and solitons. We also find that pre-strains and the geometrical size can have some important influences. The interactions of transformation fronts and rarefaction waves (which have not been considered in literature before) are investigated and some interesting phenomena are found.

Original language	English
Title of host publication	SMART DEVICES: MODELING OF MATERIAL SYSTEMS
Editors	SM Sivakumar, Buravalla, AR Srinivasa
Publisher	American Institute of Physics
Pages	77-+
Number of pages	3
ISBN (Print)	978-0-7354-0553-0
Publication status	Published - 2008
Event	International Workshop on Smart Devices - Modeling of Material Systems - Chennai, India Duration: 10 Jan 2008 → 12 Jan 2008

Publication series

Name	AIP Conference Proceedings
Publisher	AMER INST PHYSICS
Volume	1029
ISSN (Print)	0094-243X

Conference

Conference	International Workshop on Smart Devices - Modeling of Material Systems
Place	India
City	Chennai
Period	10/01/08 → 12/01/08

Funding

The Work describle in this is fully supported by a Grant from the Research Grants Council of Hong Kong SAR (project No:City U100804)and a stategic grant from City University of Hong Kong (project:7001645)

Research Keywords

nonlinear waves
solid-solid phase transition
WENO scheme
elastic cylinder
ESSENTIALLY NONOSCILLATORY SCHEMES
PHASE-TRANSFORMING MATERIALS
INDUCED TENSILE WAVES
CONSERVATION-LAWS
HIGH-ORDER
KINETIC RELATIONS
MIXED-TYPE
PROPAGATION
TRANSITIONS
MODEL

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@inproceedings{49d88cc3377f4bf4a115f7711276bf7d,

title = "Impact-induced wave patterns in a slender cylinder composed of a non-convex elastic material",

abstract = "This paper studies nonlinear wave propagation in a slender elastic cylinder due to impacts. One purpose is to examine what kinds of wave patterns can arise when both the material nonlinearity caused by a non-convex energy function and the dispersion caused by the lateral movement are present. A high-order weighted essentially non-oscillatory (WENO) scheme is used to obtain the numerical solutions of a model equation which takes into account the dispersion and the above-mentioned nonlinearity. It turns out that a variety of wave patterns can appear, including the co-existence of a transformation front and solitons. We also find that pre-strains and the geometrical size can have some important influences. The interactions of transformation fronts and rarefaction waves (which have not been considered in literature before) are investigated and some interesting phenomena are found.",

keywords = "nonlinear waves, solid-solid phase transition, WENO scheme, elastic cylinder, ESSENTIALLY NONOSCILLATORY SCHEMES, PHASE-TRANSFORMING MATERIALS, INDUCED TENSILE WAVES, CONSERVATION-LAWS, HIGH-ORDER, KINETIC RELATIONS, MIXED-TYPE, PROPAGATION, TRANSITIONS, MODEL",

author = "Hui-Hui Dai and Zhenli Xu",

year = "2008",

language = "English",

isbn = "978-0-7354-0553-0",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics",

pages = "77--+",

editor = "SM Sivakumar and Buravalla and AR Srinivasa",

booktitle = "SMART DEVICES: MODELING OF MATERIAL SYSTEMS",

address = "United States",

note = "International Workshop on Smart Devices - Modeling of Material Systems ; Conference date: 10-01-2008 Through 12-01-2008",

}

Dai, H-H & Xu, Z 2008, Impact-induced wave patterns in a slender cylinder composed of a non-convex elastic material. in SM Sivakumar, Buravalla & AR Srinivasa (eds), SMART DEVICES: MODELING OF MATERIAL SYSTEMS. AIP Conference Proceedings, vol. 1029, American Institute of Physics, pp. 77-+, International Workshop on Smart Devices - Modeling of Material Systems, Chennai, India, 10/01/08.

Impact-induced wave patterns in a slender cylinder composed of a non-convex elastic material. / Dai, Hui-Hui; Xu, Zhenli.
SMART DEVICES: MODELING OF MATERIAL SYSTEMS. ed. / SM Sivakumar; Buravalla; AR Srinivasa. American Institute of Physics, 2008. p. 77-+ (AIP Conference Proceedings; Vol. 1029).

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

TY - GEN

T1 - Impact-induced wave patterns in a slender cylinder composed of a non-convex elastic material

AU - Dai, Hui-Hui

AU - Xu, Zhenli

PY - 2008

Y1 - 2008

N2 - This paper studies nonlinear wave propagation in a slender elastic cylinder due to impacts. One purpose is to examine what kinds of wave patterns can arise when both the material nonlinearity caused by a non-convex energy function and the dispersion caused by the lateral movement are present. A high-order weighted essentially non-oscillatory (WENO) scheme is used to obtain the numerical solutions of a model equation which takes into account the dispersion and the above-mentioned nonlinearity. It turns out that a variety of wave patterns can appear, including the co-existence of a transformation front and solitons. We also find that pre-strains and the geometrical size can have some important influences. The interactions of transformation fronts and rarefaction waves (which have not been considered in literature before) are investigated and some interesting phenomena are found.

AB - This paper studies nonlinear wave propagation in a slender elastic cylinder due to impacts. One purpose is to examine what kinds of wave patterns can arise when both the material nonlinearity caused by a non-convex energy function and the dispersion caused by the lateral movement are present. A high-order weighted essentially non-oscillatory (WENO) scheme is used to obtain the numerical solutions of a model equation which takes into account the dispersion and the above-mentioned nonlinearity. It turns out that a variety of wave patterns can appear, including the co-existence of a transformation front and solitons. We also find that pre-strains and the geometrical size can have some important influences. The interactions of transformation fronts and rarefaction waves (which have not been considered in literature before) are investigated and some interesting phenomena are found.

KW - nonlinear waves

KW - solid-solid phase transition

KW - WENO scheme

KW - elastic cylinder

KW - ESSENTIALLY NONOSCILLATORY SCHEMES

KW - PHASE-TRANSFORMING MATERIALS

KW - INDUCED TENSILE WAVES

KW - CONSERVATION-LAWS

KW - HIGH-ORDER

KW - KINETIC RELATIONS

KW - MIXED-TYPE

KW - PROPAGATION

KW - TRANSITIONS

KW - MODEL

M3 - RGC 32 - Refereed conference paper (with host publication)

SN - 978-0-7354-0553-0

T3 - AIP Conference Proceedings

SP - 77-+

BT - SMART DEVICES: MODELING OF MATERIAL SYSTEMS

A2 - Sivakumar, SM

A2 - Buravalla, null

A2 - Srinivasa, AR

PB - American Institute of Physics

T2 - International Workshop on Smart Devices - Modeling of Material Systems

Y2 - 10 January 2008 through 12 January 2008

ER -

Impact-induced wave patterns in a slender cylinder composed of a non-convex elastic material

Abstract

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Research Keywords

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