zbMATH — the first resource for mathematics

Modelling the smooth muscle tissue as a dissipative microstructured material. (English) Zbl 1189.74086
Ganghoffer, Jean-François (ed.) et al., Mechanics of microstructured solids. Cellular materials, fibre-reinforced solids and soft tissues. Papers based on the presentations at the 11th EUROMECH-MECAMAT conference, Torino, Italy, March 10–14, 2008. Berlin: Springer (ISBN 978-3-642-00910-5/hbk; 978-3-642-00911-2/ebook). Lecture Notes in Applied and Computational Mechanics 46, 101-108 (2009).
Summary: A highly simplified model of the smooth muscle tissue is formed to study a special form of viscous effects occurring in living tissues. Namely, when a sample of the tissue is deformed, the fluid in the extracellular matrix has to move because it is extruded from one places into others. This phenomenon contributes into the global viscous properties of the tissue. That contribution is studied by means of a simplified model of smooth muscle tissue regarded as a regular lattice of elastic inclusions. An expression of the dissipation due to the fluid flow around the inclusions is found out. At the macroscopic (continuum) level, the idea of constitutive model with internal variables is used. As a result, a differential form of the viscoelastic behaviour is derived. The model is solved numerically and fitted by a confrontation with experiment performed on gastropod smooth muscle tissue.
For the entire collection see [Zbl 1189.74006].

74L15 Biomechanical solid mechanics
92C10 Biomechanics
Full Text: DOI