On the Fiber Stretch in Shearing Deformations of Fibrous Soft Materials
Source abstract
Abstract
The behavior of the fiber stretch in simple shear of soft materials fiber-reinforced with a single family of oriented parallel fibers is examined. The analysis is purely kinematical and the results are valid for both compressible and incompressible materials. It is shown that for a given amount of shear, for all fiber orientation angles in the range (0 < heta < pi /4), the fiber stretch increases with increasing ( heta) whereas in the range (pi /4 < heta < pi /2), this is no longer the case and there is a particular fiber orientation for which the fiber stretch is a maximum. For a particular amount of shear corresponding to a special angle of shear (a “magic” angle of (35.26circ)), the fiber-orientation angle at which the fiber stretch is a maximum is its geometric complement namely a magic angle of (54.74circ). The results are also valid for torsion of a circular cylinder reinforced with a single family of helically wound fibers.
Source: expertdata · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Elasticity and Material Modeling · Elasticity and Wave Propagation · Composite Material Mechanics
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (15)
Show source-provided references
1. Moreira, C.S., Nunes, L.C.S.: Simple shearing of rubberlike materials filled with parallel fibers at large strain. J. Compos. Mater. 51, 1643–1651 (2017)10.1177/0021998316658537 ↗
2. Horgan, C.O., Murphy, J.G.: Simple shearing of soft biological tissues. Proc. R. Soc. A 467, 760–777 (2011)10.1098/rspa.2010.0288 ↗
3. Horgan, C.O., Murphy, J.G.: Fiber orientation effects in simple shearing of fibrous soft tissues. J. Biomech. 64, 131–135 (2017)10.1016/j.jbiomech.2017.09.018 ↗
4. Jacobs, N.T., Smith, L.J., Han, W.M., Morelli, J., Yoder, J.H., Elliott, D.M.: Effect of orientation and targeted extracellular matrix degradation on the shear mechanical properties of the annulus fibrosus. J. Mech. Behav. Biomed. Mater. 4, 1611–1619 (2011)10.1016/j.jmbbm.2011.03.016 ↗
5. Driscoll, T.P., Nerurkar, N.L., Jacobs, N.T., Elliott, D.M., Mauck, R.L.: Fiber angle and aspect ratio influence the shear mechanics of oriented electrospun nanofibrous scaffolds. J. Mech. Behav. Biomed. Mater. 4, 1627–1636 (2011)10.1016/j.jmbbm.2011.03.022 ↗
6. Feng, Y., Okamoto, R.J., Namani, R., Genin, G.M., Bayly, P.V.: Measurements of mechanical anisotropy in brain tissue and implications for transversely isotropic material models of white matter. J. Mech. Behav. Biomed. Mater. 23, 117–132 (2013)10.1016/j.jmbbm.2013.04.007 ↗
7. Feng, Y., Okamoto, R.J., Genin, G.M., Bayly, P.V.: On the accuracy and fitting of transversely isotropic material models. J. Mech. Behav. Biomed. Mater. 61, 554–566 (2016)10.1016/j.jmbbm.2016.04.024 ↗
8. Qiu, G.Y., Pence, T.J.: Remarks on the behavior of simple directionally reinforced incompressible nonlinearly elastic solids. J. Elast. 49, 1–30 (1997)10.1023/A:1007410321319 ↗
9. Merodio, J., Ogden, R.W.: Mechanical response of fiber-reinforced incompressible non-linearly elastic solids. Int. J. Non-Linear Mech. 40, 213–227 (2005)10.1016/j.ijnonlinmec.2004.05.003 ↗
10. Horgan, C.O., Murphy, J.G.: Simple shearing of incompressible and slightly compressible isotropic nonlinearly elastic materials. J. Elast. 98, 205–221 (2010)10.1007/s10659-009-9225-1 ↗
11. Goriely, A., Tabor, M.: Rotation, inversion and perversion in anisotropic elastic cylindrical tubes and membranes. Proc. R. Soc. A 469, 20130011 (2013)10.1098/rspa.2013.0011 ↗
12. Demirkoparan, H., Pence, T.J.: Magic angles for fiber reinforcement in rubber-elastic tubes subject to pressure and swelling. Int. J. Non-Linear Mech. 68, 87–95 (2015)10.1016/j.ijnonlinmec.2014.05.008 ↗
13. Goriely, A.: The Mathematics and Mechanics of Biological Growth. Springer, New York (2017)10.1007/978-0-387-87710-5 ↗
14. Horgan, C.O., Murphy, J.G.: Magic angles for fibrous incompressible elastic materials. Proc. R. Soc. A 474, 20170728 (2018)10.1098/rspa.2017.0728 ↗
15. Horgan, C.O., Murphy, J.G.: Reverse Poynting effects in the torsion of soft biomaterials. J. Elast. 118, 127–140 (2015)10.1007/s10659-014-9482-5 ↗