When a block made of an elastomer is subjected to a large shear, its surface remains flat. When a block of biological soft tissue is subjected to a large shear, it is likely that its surface in the plane of shear will buckle (appearance of wrinkles). One factor that distinguishes soft tissues from rubberlike solids is the presence—sometimes visible to the naked eye—of oriented collagen fiber bundles, which are stiffer than the elastin matrix into which they are embedded but are nonetheless flexible and extensible. Here we show that the simplest model of isotropic nonlinear elasticity, namely, the incompressible neo-Hookean model, suffers surface instability in shear only at tremendous amounts of shear, i.e., above 3.09, which corresponds to a angle of shear. Next we incorporate a family of parallel fibers in the model and show that the resulting solid can be either reinforced or strongly weakened with respect to surface instability, depending on the angle between the fibers and the direction of shear and depending on the ratio between the stiffness of the fibers and that of the matrix. For this ratio we use values compatible with experimental data on soft tissues. Broadly speaking, we find that the surface becomes rapidly unstable when the shear takes place “against” the fibers and that as increases, so does the sector of angles where early instability is expected to occur.
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December 2008
Research Papers
Surface Instability of Sheared Soft Tissues
M. Destrade,
M. Destrade
School of Electrical, Electronic, and Mechanical Engineering,
University College Dublin
, Belfield, Dublin 4, Ireland
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M. D. Gilchrist,
M. D. Gilchrist
School of Electrical, Electronic, and Mechanical Engineering,
University College Dublin
, Belfield, Dublin 4, Ireland
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D. A. Prikazchikov,
D. A. Prikazchikov
Department of Advanced and Applied Mathematics,
The Russian State Open Technical University of Railway Transport
, Chasovaya Street, Moscow 22∕2, Russia
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G. Saccomandi
G. Saccomandi
Dipartimento di Ingegneria Industriale,
Università degli Studi di Perugia
, 06125 Perugia, Italy
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M. Destrade
School of Electrical, Electronic, and Mechanical Engineering,
University College Dublin
, Belfield, Dublin 4, Ireland
M. D. Gilchrist
School of Electrical, Electronic, and Mechanical Engineering,
University College Dublin
, Belfield, Dublin 4, Ireland
D. A. Prikazchikov
Department of Advanced and Applied Mathematics,
The Russian State Open Technical University of Railway Transport
, Chasovaya Street, Moscow 22∕2, Russia
G. Saccomandi
Dipartimento di Ingegneria Industriale,
Università degli Studi di Perugia
, 06125 Perugia, ItalyJ Biomech Eng. Dec 2008, 130(6): 061007 (6 pages)
Published Online: October 10, 2008
Article history
Received:
March 13, 2008
Revised:
April 22, 2008
Published:
October 10, 2008
Citation
Destrade, M., Gilchrist, M. D., Prikazchikov, D. A., and Saccomandi, G. (October 10, 2008). "Surface Instability of Sheared Soft Tissues." ASME. J Biomech Eng. December 2008; 130(6): 061007. https://doi.org/10.1115/1.2979869
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