On Compatible Strain with Reference to Biomechanics
2005 (English)In: Zeitschrift für Angewandte Mathematik und Mechanik, ISSN 0044-2267 (print), 1521-4001 (online), Vol. 85, no 6, 440-448 p.Article in journal (Refereed) Published
In previous studies, residual stresses and strains in soft tissues have been experimentally investigated by cutting the material into pieces that are assumed to become stress free. The present paper gives a theoretical basis for such a procedure, based on a classical theorem of continuum mechanics. As applications of the theory we study rotationally symmetric cylinders and spheres. A computer algebra system is used to state and solve differential equations that define compatible strain distributions. A mapping previously used in constructing a mathematical theory for the mechanical behavior of arteries is recovered as a corollary of the theory, but is found not to be unique. It is also found, for a certain residual strain distribution, that a sphere can be cut from pole to pole to form a stress and strain free configuration.
Place, publisher, year, edition, pages
2005. Vol. 85, no 6, 440-448 p.
biomechanics, compatible strain, curvature tensor, elasticity, residual stress, soft tissue
National CategoryEngineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-14329DOI: 10.1002/zamm.200410192OAI: oai:DiVA.org:liu-14329DiVA: diva2:23256