Uniqueness of equilibrium solutions in second-order gradient nonlinear elasticity

Anita Mareno

doi:10.1023/B:ELAS.0000033865.03618.e0

Uniqueness of equilibrium solutions in second-order gradient nonlinear elasticity

Anita Mareno

School of Science, Engineering & Technology (Harrisburg)

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We consider a three-dimensional elastic body whose material response function depends not only on the gradient of the deformation, but also on its second gradient. Using the elastic energy-momentum tensor as derived by Eshelby 2 we generalize a well-known uniqueness result of Knops and Stuart 8 for a Dirichlet boundary value problem associated with this response function.

Original language	English (US)
Pages (from-to)	99-107
Number of pages	9
Journal	Journal of Elasticity
Volume	74
Issue number	2
DOIs	https://doi.org/10.1023/B:ELAS.0000033865.03618.e0
State	Published - Feb 2004

All Science Journal Classification (ASJC) codes

General Materials Science
Mechanics of Materials
Mechanical Engineering

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10.1023/B:ELAS.0000033865.03618.e0

Cite this

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title = "Uniqueness of equilibrium solutions in second-order gradient nonlinear elasticity",

abstract = "We consider a three-dimensional elastic body whose material response function depends not only on the gradient of the deformation, but also on its second gradient. Using the elastic energy-momentum tensor as derived by Eshelby 2 we generalize a well-known uniqueness result of Knops and Stuart 8 for a Dirichlet boundary value problem associated with this response function.",

author = "Anita Mareno",

note = "Funding Information: This work was supported in part by the National Science Foundation through grant DMS-0072514. We also note that this work was originally written at the Center for Applied Mathematics, Cornell University and was revised while the author was at the Department of Mathematics, Cornell University.",

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PY - 2004/2

Y1 - 2004/2

N2 - We consider a three-dimensional elastic body whose material response function depends not only on the gradient of the deformation, but also on its second gradient. Using the elastic energy-momentum tensor as derived by Eshelby 2 we generalize a well-known uniqueness result of Knops and Stuart 8 for a Dirichlet boundary value problem associated with this response function.

AB - We consider a three-dimensional elastic body whose material response function depends not only on the gradient of the deformation, but also on its second gradient. Using the elastic energy-momentum tensor as derived by Eshelby 2 we generalize a well-known uniqueness result of Knops and Stuart 8 for a Dirichlet boundary value problem associated with this response function.

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U2 - 10.1023/B:ELAS.0000033865.03618.e0

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M3 - Article

AN - SCOPUS:3142722166

SN - 0374-3535

VL - 74

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EP - 107

JO - Journal of Elasticity

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IS - 2

ER -

Uniqueness of equilibrium solutions in second-order gradient nonlinear elasticity

Abstract

All Science Journal Classification (ASJC) codes

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