Morphology of residually stressed tubular tissues: Beyond the elastic multiplicative decomposition

P. Ciarletta; M. Destrade; A. L. Gower; M. Taffetani

doi:10.1016/j.jmps.2016.02.020

Morphology of residually stressed tubular tissues: Beyond the elastic multiplicative decomposition

P. Ciarletta^*
, M. Destrade
, A. L. Gower
, M. Taffetani

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

57 Citations (Scopus)

Abstract

Many interesting shapes appearing in the biological world are formed by the onset of mechanical instability. In this work we consider how the build-up of residual stress can cause a solid to buckle. In all past studies a fictitious (virtual) stress-free state was required to calculate the residual stress. In contrast, we use a model which is simple and allows the prescription of any residual stress field. We specialize the analysis to an elastic tube subject to a two-dimensional residual stress, and find that incremental wrinkles can appear on its inner or its outer face, depending on the location of the highest value of the residual hoop stress. We further validate the predictions of the incremental theory with finite element simulations, which allow us to go beyond this threshold and predict the shape, number and amplitude of the resulting creases.

Original language	English
Pages (from-to)	242-253
Number of pages	12
Journal	Journal of the Mechanics and Physics of Solids
Volume	90
DOIs	https://doi.org/10.1016/j.jmps.2016.02.020
Publication status	Published - 1 May 2016

Bibliographical note

Funding Information:
Partial funding by the "Start-up Packages and PhD Program" project, co-funded by Regione Lombardia through the "Fondo perlosviluppoelacoesione 2007-2013", formerly FAS program, is gratefully acknowledged. Sois the support from the Irish Research Council and the EPSRC (referenceEP/M026205/1).

Funding Information:
Partial funding by the “Start-up Packages and PhD Program” project, co-funded by Regione Lombardia through the “Fondo per lo sviluppo e la coesione 2007–2013”, formerly FAS program, is gratefully acknowledged. So is the support from the Irish Research Council and the EPSRC (reference EP/M026205/1 ).

Publisher Copyright:
© 2016 Elsevier Ltd. All rights reserved.

Research Groups and Themes

Engineering Mathematics Research Group

Keywords

Finite elements
Nonlinear elasticity
Post-buckling
Residual stress
Soft tube
Stability analysis

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title = "Morphology of residually stressed tubular tissues: Beyond the elastic multiplicative decomposition",

abstract = "Many interesting shapes appearing in the biological world are formed by the onset of mechanical instability. In this work we consider how the build-up of residual stress can cause a solid to buckle. In all past studies a fictitious (virtual) stress-free state was required to calculate the residual stress. In contrast, we use a model which is simple and allows the prescription of any residual stress field. We specialize the analysis to an elastic tube subject to a two-dimensional residual stress, and find that incremental wrinkles can appear on its inner or its outer face, depending on the location of the highest value of the residual hoop stress. We further validate the predictions of the incremental theory with finite element simulations, which allow us to go beyond this threshold and predict the shape, number and amplitude of the resulting creases.",

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N1 - Funding Information: Partial funding by the "Start-up Packages and PhD Program" project, co-funded by Regione Lombardia through the "Fondo perlosviluppoelacoesione 2007-2013", formerly FAS program, is gratefully acknowledged. Sois the support from the Irish Research Council and the EPSRC (referenceEP/M026205/1). Funding Information: Partial funding by the “Start-up Packages and PhD Program” project, co-funded by Regione Lombardia through the “Fondo per lo sviluppo e la coesione 2007–2013”, formerly FAS program, is gratefully acknowledged. So is the support from the Irish Research Council and the EPSRC (reference EP/M026205/1 ). Publisher Copyright: © 2016 Elsevier Ltd. All rights reserved.

PY - 2016/5/1

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N2 - Many interesting shapes appearing in the biological world are formed by the onset of mechanical instability. In this work we consider how the build-up of residual stress can cause a solid to buckle. In all past studies a fictitious (virtual) stress-free state was required to calculate the residual stress. In contrast, we use a model which is simple and allows the prescription of any residual stress field. We specialize the analysis to an elastic tube subject to a two-dimensional residual stress, and find that incremental wrinkles can appear on its inner or its outer face, depending on the location of the highest value of the residual hoop stress. We further validate the predictions of the incremental theory with finite element simulations, which allow us to go beyond this threshold and predict the shape, number and amplitude of the resulting creases.

AB - Many interesting shapes appearing in the biological world are formed by the onset of mechanical instability. In this work we consider how the build-up of residual stress can cause a solid to buckle. In all past studies a fictitious (virtual) stress-free state was required to calculate the residual stress. In contrast, we use a model which is simple and allows the prescription of any residual stress field. We specialize the analysis to an elastic tube subject to a two-dimensional residual stress, and find that incremental wrinkles can appear on its inner or its outer face, depending on the location of the highest value of the residual hoop stress. We further validate the predictions of the incremental theory with finite element simulations, which allow us to go beyond this threshold and predict the shape, number and amplitude of the resulting creases.

KW - Finite elements

KW - Nonlinear elasticity

KW - Post-buckling

KW - Residual stress

KW - Soft tube

KW - Stability analysis

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DO - 10.1016/j.jmps.2016.02.020

M3 - Article (Academic Journal)

AN - SCOPUS:84961828021

SN - 0022-5096

VL - 90

SP - 242

EP - 253

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

ER -

Morphology of residually stressed tubular tissues: Beyond the elastic multiplicative decomposition

Abstract

Bibliographical note

Research Groups and Themes

Keywords

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