Torsion in Microstructure Hollow Thick-Walled Circular Cylinder Made up of Orthotropic Material

Document Type : Research Paper


Department of Mathematics, Jaypee Institute of Information Technology, Noida, India


In this paper, a numerical solution has been developed for hollow circular cylinders made up of orthotropic material which is subjected to twist using micro polar theory. The effect of twisting moment and material internal length on hollow thick-walled circular cylinder made up of micro polar orthotropic material is investigated. Finite difference method has been used to exhibit the influence of shear moduli and material internal length on shear stresses and couple stresses. It is found that the effect of small characteristic length on shear stresses is negligible and couple stresses present its significance when characteristic length is large in solid particle. The behavior of couple stresses are nonlinear for large internal length while for small internal length couple stresses are linear in nature except near the free boundaries. Torsion in hollow cylinder made up of micro polar orthotropic play vital role in the presence of cracks and holes. Therefore, torsional analysis of hollow cylinder plays important role in the field of biomechanics.


[1] Pagano N.J., Sih G.C., 1968, Stress singularities around a crack in a cosserat plate, International Journal of Solids and Structures 4(5): 531-553.
[2] Fatemi J., Onck P.R., Poort G., van Keulen F., 2003, Cosserat moduli of anisotropic cancellous bone: A micromechanical analysis, Journal de Physique IV 105: 273-280.
[3] Eringen A.C., 1966, Linear theory of micropolar elasticity, Journal of Mathematics and Mechanics 15: 909-923.
[4] Eringen A.C., 1999, Microcontinuum Field Theories, Springer, Berlin edition.
[5] Altenbach H., Eremeyev V.A., 2010, Thin-walled structures made of foams, Cellular and Porous Materials in Structures and Processes 2010: 167-242.
[6] Gauthier R.D., Jahsman W.E., 1975, A quest for micropolar elastic constants, Journal of Applied Mechanics 42(2): 369-374.
[7] Merkel A., Tournat V., Gusev V., 2011, Experimental evidence of rotational elastic waves in granular phononic crystals, Physical Review Letters 107(22): 225502.
[8] Kvasov R., Steinberg L., 2013, Numerical modeling of bending of micropolar plates, Thin-Walled Structures 69: 67-78.
[9] Hadjesfandiari A.R., Dargush G.F., 2014, Evolution of generalized couple-stress continuum theories: A critical analysis, Physics 2014:1501.03112.
[10] Hadjesfandiari A.R., Dargush G.F., 2013, Fundamental solutions for isotropic size-dependent couple stress elasticity, International Journal of Solids and Structures 50(9): 1253-1265.
[11] Taliercio A., Veber D., 2009, Some problems of linear elasticity for cylinders in micropolar orthotropic material, International Journal of Solids and Structures 46(22): 3948-3963.
[12] Taliercio A., 2010, Torsion of micropolar hollow circular cylinders, Mechanics Research Communications 37(4): 406-411.
[13] Sharma S., Yadav S., Sharma R., 2015, Thermal creep analysis of functionally graded thick-walled cylinder subjected to torsion and internal and external pressure, Journal of Solid Mechanics 9(2): 302-318.
[14] Taliercio A., Veber D., 2016, Torsion of elastic anisotropic micropolar cylindrical bars, European Journal of Mechanics-A/Solids 55: 45-56.
[15] Smith A., 1970, Torsion and vibrations of cylinders of a micropolar elastic solid, Recent Advances in Engineering Science 5:129-137.
[16] Reddy G.V.K., Venkatasubramanian N.K., 1976, Saint-venant's problem for a micropolar elastic circular cylinder, International Journal of Engineering Science 14(11): 1047-1057.
[17] Eringen A.C., 1968,Theory of Micropolar Elasticity, New York, Academic Press.