liu.seSearch for publications in DiVA
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Boundary Value Problems of an Initially Stressed Body
Linköping University, Department of Mechanical Engineering, Engineering Mechanics. Linköping University, The Institute of Technology.
Linköping University, Department of Mechanical Engineering, Engineering Mechanics. Linköping University, The Institute of Technology.ORCID iD: 0000-0001-8460-0131
2004 (English)Report (Other academic)
Abstract [en]

The initial strain in a body can be described by a two-point tensor that maps tangent vectors between a local stress free configuration (manifolds) and the initially strained configuration. The initial strain tensor can be used to form a metric tensor and this metric can be used to induce a third manifold. The boundary value problem of an elastic body is in this paper formulated on these three manifolds: the induced manifold, the initially strained configuration and the local stress free configuration. Moreover, we consider a hyperelastic body with incompressible properties and we show that in that case, the divergence of the first Piola- Kirchhoff stress tensor defined on the initially strained configuration and on the induced manifold coincide. There-fore, we conclude that for an incompressible material, the boundary value problems stated on the initially strained configuration and on the induced manifold are the same.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet , 2004. , 17 p.
Series
LITH-IKP-R, ISSN 0281-5001 ; 1348
Keyword [en]
Boundary, Value, Problems Initially Stressed Body
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-22424Local ID: 1640OAI: oai:DiVA.org:liu-22424DiVA: diva2:242737
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2017-05-15
In thesis
1. Modeling Residual Stress Fields in Soft Tissues with Application to Human Arteries
Open this publication in new window or tab >>Modeling Residual Stress Fields in Soft Tissues with Application to Human Arteries
2004 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Biomechanics or Mechanics of Biology comprises many different fields. This thesis deals with soft tissues or living tissues and the fact that these materials live in a pressurized environment. This means that an unloaded tissue may not be stress free. The stress in an unloaded body is usually called residual stress. This thesis consist of an introduction to continuum mechanics and to soft tissues, and three research papers.

The first paper deals with a zero stress configuration and the question of compatibility. It is shown that the zero stress configuration not necessarily constitutes a compatible body. The condition for compatibility is analyzed and exemplified on a cylinder and a sphere.

In the second paper a model for residually stressed arteries based on local deformations is developed. The material properties for a human aorta is identified by the solution to an optimization problem. The resulting initial strains show a non constant behavior and this behavior cannot be described by the commonly used opening- angle model.

The last paper is about formulating boundary value problems for initially stressed bodies in three different reference configurations. Firstly, the equilibrium equation and constitutive relation are stated on the unloaded residually stressed body. Secondly, all material points are relieved from stress by a tangent map and the new stress free configuration, which may be incompatible, is used to state the boundary value problem. Thirdly; we use the relieving tangent map to induce a new metric on the body. This induced metric is in general non Euclidean. Finally, we formulate the boundary value problem on this manifold.

Place, publisher, year, edition, pages
Linköping: Linköpings universitet, 2004. 40 p.
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1118
Series
LiU-TEK-LIC, 47
Keyword
Continuum Mechanics, Modeling, Residual Stress, Soft Tissues
National Category
Engineering and Technology
Identifiers
urn:nbn:se:liu:diva-22418 (URN)1633 (Local ID)91-85295-48-5 (ISBN)1633 (Archive number)1633 (OAI)
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2013-11-12

Open Access in DiVA

No full text

Authority records BETA

Olsson, TobiasKlarbring, Anders

Search in DiVA

By author/editor
Olsson, TobiasKlarbring, Anders
By organisation
Engineering MechanicsThe Institute of Technology
Engineering and Technology

Search outside of DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric score

urn-nbn
Total: 47 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf