Morphology of residually stressed tubular tissues: Beyond the elastic multiplicative decomposition
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 s...
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| Published in | Journal of the mechanics and physics of solids Vol. 90; pp. 242 - 253 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.05.2016
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0022-5096 1873-4782 |
| DOI | 10.1016/j.jmps.2016.02.020 |
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| 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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| AbstractList | 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. 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. |
| Author | Taffetani, M. Destrade, M. Ciarletta, P. Gower, A.L. |
| Author_xml | – sequence: 1 givenname: P. surname: Ciarletta fullname: Ciarletta, P. email: pasquale.ciarletta@polimi.it, pasquale.ciarletta@upmc.fr organization: Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190, Institut Jean Le Rond d'Alembert, F-75005 Paris, France – sequence: 2 givenname: M. surname: Destrade fullname: Destrade, M. organization: School of Mathematics, Statistics and Applied Mathematics, NUI Galway, University Road, Galway, Ireland – sequence: 3 givenname: A.L. surname: Gower fullname: Gower, A.L. organization: School of Mathematics, Statistics and Applied Mathematics, NUI Galway, University Road, Galway, Ireland – sequence: 4 givenname: M. surname: Taffetani fullname: Taffetani, M. organization: MOX – Politecnico di Milano, piazza Leonardo da Vinci 32, 20133 Milano, Italy |
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| Keywords | Post-buckling Finite elements Stability analysis Soft tube Nonlinear elasticity Residual stress Finite Elements |
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| SubjectTerms | Fasteners Finite elements Hoop stress Instability Mathematical analysis Mathematics Nonlinear elasticity Physics Post-buckling Residual stress Simulation Soft tube Stability analysis Tubes Two dimensional |
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| Title | Morphology of residually stressed tubular tissues: Beyond the elastic multiplicative decomposition |
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