Abstract
Since stress fibers have micro-size dimensions, their biomechanical behavior should demand mechanical models conforming with gradient strain deformation theories. In particular, the torsion and the stretching of stress fibers are discussed into the context of strain gradient elasticity theory and their size effects. It is proven for the torsion problem that the torsion moment varies with the axial length of the bar for constant twist angle, whereas for the simple tension problem, the strain is non-uniform along the stress fiber. The proposed theory is supported by experimental evidence.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aifantis E.C.: Strain gradient interpretation of size effects. Int. J. Fract. 95, 299–314 (1999)
Aifantis E.C.: Update on a class of gradient theories. Mech. Mater. 35, 259–280 (2003)
Besser A., Schwarz U.S.: Coupling biochemistry and mechanics in cell adhesion: a model for inhomogeneous stress fiber contraction. New J. Phys. 9, 425–452 (2007)
Cosserat E., Cosserat F.: Theories des Corpes Deformables. A. Hermann et Fils, Paris (1909)
Fleck N.A., Hutchinson J.W.: Strain gradient plasticity. Adv. Appl. Mech. 33, 295–361 (1997)
Fleck N.A., Muller G.M., Ashby M.F., Hutchinson J.W.: Strain gradient plasticity: theory and experiment. Acta Metall. Matter. 42(2), 475–487 (1994)
Holzapfel G.A., Ogden R.W.: On the bending and stretching elasticityof biopolymer filaments. J. Elast. 104, 319–342 (2011)
Huxley A.F.: Musle structure and theories of contraction. Prog. Biophys. Chem. 7, 255–318 (1957)
Janmey P.A., Soren H., Kas J., Lerche D., Maggs A., Sackmann E., Schliva M., Stossel T.P.: The mechanical properties of actin gels. J. Biol. Chem. 269(51), 32503–32513 (1994)
Janmey P.A.: Mechanical properties of cytoskeletal polymers. Curr. Opin. Cell Biol. 2, 4–11 (1991)
Lazopoulos K.A., Pirentis A.: Substrate stretching and reorganization of stress fibers as a finite elasticity problem. Int. J. Solids Struct. 44(25-26), 8285–8296 (2007)
Lazopoulos K.A., Stamenovic D.: Durotaxis as an elastic stability phenomenon. J. Biomech. 41(6), 1289–1294 (2008)
Mindlin R.D.: Second gradient of strain and surface tension in linear elsticity. Int. J. Solids Struct. 1, 417–438 (1965)
Morfat M.R.K., Kamm R.D.: Cytoskeletal Mechanics, Models and Measurements. Cambridge University Press, Cambridge (2006)
Peterson L.J., Rajfur Z., Maddox A.S., Freel C.D., Chen Y., Edlund M., Otey C., Burridge K.: Simultaneous stretching and contraction of stress fibers in vivo. Mol. Biol. Cell 15, 3497–3508 (2004)
Stamenovic D., Lazopoulos K.A., Pirentis A., Suki B.: Mechanical stability determines stress fiber and focal adhesion orientation. Cell. Mol. Bioeng. 2(4), 475–485 (2009)
Sternberg E., Knowles J.K.: Minimum energy characterizations of Saint-Venant’s solution for the relaxed Saint-Venent problem. Arch. Ration. Mech. Anal. 21, 89–107 (1966)
Toupin R.A.: Elastic materials with couple stress. Arch. Ration. Mech. Anal. 11, 385–414 (1962)
Toupin R.A.: Saint Venant’s principle. Arch. Ration. Mech. Anal. 18, 83–96 (1965)
Vardoulakis, I.: Linear micro-elasticity. In: Darve, F., Vardoulakis, I. (eds.) Degradations and Instabilities in Geomaterials. CISM/DIGA- sponsored course, Springer, Chapter 4 (2004)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lazopoulos, K.A., Lazopoulos, A.K. Strain gradient elasticity and stress fibers. Arch Appl Mech 83, 1371–1381 (2013). https://doi.org/10.1007/s00419-013-0752-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-013-0752-7