Dresden 2014 – scientific programme
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BP: Fachverband Biologische Physik
BP 11: Posters: Cytoskeleton
BP 11.9: Poster
Tuesday, April 1, 2014, 09:30–12:30, P1
Nonlinear elasticity of cross-linked networks — •Karin John1, Denis Caillerie2, Philippe Peyla1, Annie Raoult3, and Chaouqi Misbah1 — 1Université Grenoble 1/CNRS, LIPhy UMR 5588, F-38041 Grenoble, France — 2L3S-R, B.P. 53, F-38041 Grenoble Cedex 9, France — 3Laboratoire MAP5 UMR 8145, Université Paris Descartes/CNRS, F-75270 Paris Cedex 06, France
Cross-linked semiflexible polymer networks are omnipresent in living cells. Typical examples are actin networks in the cytoplasm of eukaryotic cells, which play an essential role in cell motility, and the spectrin network, a key element in maintaining the integrity of erythrocytes in the blood circulatory system. We introduce a simple mechanical network model at the length scale of the typical mesh size and derive a continuous constitutive law relating the stress to deformation. The continuous constitutive law is found to be generically nonlinear even if the microscopic law at the scale of the mesh size is linear. The nonlinear bulk mechanical properties are in good agreement with the experimental data for semiflexible polymer networks, i.e., the network stiffens and exhibits a negative normal stress in response to a volume-conserving shear deformation, whereby the normal stress is of the same order as the shear stress. Furthermore, it shows a strain localization behavior in response to an uniaxial compression.
The presented theory provides a basis for the continuum description of polymer networks such as actin or spectrin in complex geometries and it can be easily coupled to growth problems, as they occur, for example, in modeling actin-driven motility.