Hodges, D. H., 2006, *Nonlinear Composite Beam Theory* (Progress in Astronautics and Aeronautics), 1st ed., Vol. 213, American Institute of Aeronautics and Astronautics, Inc., Reston, VA, pp. 15–17.

Campbell, A., 1912, “On Vibration Galvanometers With Unifilar Torsional Control,” Proc. Phys. Soc. London, 25(1), pp. 203–205.

[CrossRef]Pealing, H., 1913, “XLII. On an Anomalous Variation of the Rigidity of Phosphor Bronze,” Philos. Mag. Ser. 6, 25(147), pp. 418–427.

[CrossRef]Buckley, J. C., 1914, “LXXXIV. The Bifilar Property of Twisted Strips,” Philos. Mag. Ser. 6, 28(168), pp. 778–787.

[CrossRef]Wagner, H., 1936, “Torsion and Buckling of Open Sections,” National Advisory Committee for Aeronautics, Washington, DC, Technical Report No. NACA-TM-807.

Biot, M. A., 1939, “Increase of Torsional Stiffness of a Prismatical Bar Due to Axial Tension,” J. Appl. Phys., 10(12), pp. 860–864.

[CrossRef]Goodier, J. N., 1950, “Elastic Torsion in the Presence of Initial Axial Stress,” ASME J. Appl. Mech., 17(4), pp. 383–387.

Hill, R., 1959, “Some Basic Principles in the Mechanics of Solids Without a Natural Time,” J. Mech. Phys. Solids, 7(3), pp. 209–225.

[CrossRef]Houbolt, J. C., and Brooks, G. W., 1957, “Differential Equations of Motion for Combined Flapwise Bending, Chordwise Bending, and Torsion of Twisted Nonuniform Rotor Blades,” Langley Aeronautical Laboratory, Hampton, VA, Technical Report No. NACA TN 3905.

Hodges, D. H., and Dowell, E. H., 1974, “Nonlinear Equations of Motion for the Elastic Bending and Torsion of Twisted Nonuniform Rotor Blades,” Ames Research Center and U.S. Army Air Mobility R&D Laboratory, Washington, DC, Technical Report No. NASA TN D-7818.

Borri, M., and Merlini, T., 1986, “A Large Displacement Formulation for Anisotropic Beam Analysis,” Meccanica, 21(1), pp. 30–37.

[CrossRef]Fulton, M. V., and Hodges, D. H., 1993, “Aeroelastic Stability of Composite Hingeless Rotor Blades in Hover—Part I: Theory,” Math. Comput. Modell., 18(3/4), pp. 1–17.

[CrossRef]Fulton, M. V., and Hodges, D. H., 1993, “Aeroelastic Stability of Composite Hingeless Rotor Blades in Hover—Part II: Results,” Math. Comput. Modell., 18(3/4), pp. 19–35.

[CrossRef]Hodges, D. H., Harursampath, D., Volovoi, V. V., and Cesnik, C. E. S., 1999, “Non-Classical Effects in Non-Linear Analysis of Pretwisted Anisotropic Strips,” Int. J. Non Linear Mech., 34(2), pp. 259–277.

[CrossRef]Popescu, B., and Hodges, D. H., 1999, “Asymptotic Treatment of the Trapeze Effect in Finite Element Cross-Sectional Analysis of Composite Beams,” Int. J. Non Linear Mech., 34(4), pp. 709–721.

[CrossRef]Armanios, E. A., Makeev, A., and Hooke, D., 1996, “Finite-Displacement Analysis of Laminated Composite Strips With Extension-Twist Coupling,” J. Aerosp. Eng., 9(3), pp. 80–91.

[CrossRef]Cesnik, C. E. S., Hodges, D. H., Popescu, B., and Harursampath, D., 1996, “Composite Beams Cross-Sectional Modeling Including Obliqueness and Trapeze Effects,” 37th Structures, Structural Dynamics and Materials Conference, Salt Lake City, UT, Apr. 15–17, AIAA Paper No. 96-1469, pp. 1384–1397.

[CrossRef]Cesnik, C. E. S., Hodges, D. H., and Sutyrin, V. G., 1996, “Cross-Sectional Analysis of Composite Beams Including Large Initial Twist and Curvature Effects,” AIAA J., 34(9), pp. 1913–1920.

[CrossRef]Okubo, H., 1952, “The Torsion and Stretching of Spiral Rods (1st Report),” Trans. Jpn. Soc. Mech. Eng., 18(68), pp. 11–15.

[CrossRef]Okubo, H., 1953, “The Torsion and Stretching of Spiral Rods (3rd Report),” Trans. Jpn. Soc. Mech. Eng., 19(83), pp. 29–34.

[CrossRef]Chu, C., 1951, “The Effect of Initial Twist on the Torsional Rigidity of Thin Prismatical Bars and Tubular Members,” First U.S. National Congress of Applied Mechanics, National Congress of Applied Mechanics, American Society of Mechanical Engineers (ASME), Vol. 1, pp. 265–296.

Shorr, B. F., 1980, “Theory of Twisted Nonuniformly Heated Bars,” Izv. Akad. Nauk SSSR, Otd. Tekhn. Nauk Mekhan. i Mashinostr. (USSR), Washington, DC, Technical Report No. NASA-TM-7575, N80-19565.

Petersen, D., 1982, “Interaction of Torsion and Tension in Beam Theory,” Vertica, 6, pp. 311–325.

Washizu, K., 1964, “Some Considerations on Naturally Curved and Twisted Slender Beam,” J. Math. Phys., 43(2), pp. 111–116.

Ohtsuka, M., 1975, “Untwist of Rotating Blades,” ASME J. Eng. Gas Turbines Power, 97(2), pp. 180–187.

[CrossRef]Hodges, D. H., 1980, “Torsion of Pretwisted Beams Due to Axial Loading,” ASME J. Appl. Mech., 47(2), pp. 393–397.

[CrossRef]Rosen, A., 1980, “The Effect of Initial Twist on the Torsional Rigidity of Beams—Another Point of View,” ASME J. Appl. Mech., 47(2), pp. 389–392.

[CrossRef]Rosen, A., 1983, “Theoretical and Experimental Investigation of the Nonlinear Torsion and Extension of Initially Twisted Bars,” ASME J. Appl. Mech., 50(2), pp. 321–326.

[CrossRef]Rosen, A., Loewy, R. G., and Mathew, M. B., 1987, “Nonlinear Analysis of Pretwisted Rods Using Principal Curvature Transformation. I—Theoretical Derivation,” AIAA J., 25(3), pp. 470–478.

[CrossRef]Rosen, A., 1991, “Structural and Dynamic Behavior of Pretwisted Rods and Beams,” ASME Appl. Mech. Rev., 44(12), pp. 483–515.

[CrossRef]Shield, R. T., 1982, “Extension and Torsion of Elastic Bars With Initial Twist,” ASME J. Appl. Mech., 49(4), pp. 779–786.

[CrossRef]Krenk, S., 1983, “The Torsion-Extension Coupling in Pretwisted Elastic Beams,” Int. J. Solids Struct., 19(1), pp. 67–72.

[CrossRef]Krenk, S., 1983, “A Linear Theory for Pretwisted Elastic Beams,” ASME J. Appl. Mech., 50(1), pp. 137–142.

[CrossRef]Poynting, J. H., 1909, “On Pressure Perpendicular to the Shear Planes in Finite Pure Shears, and on the Lengthening of Loaded Wires When Twisted,” Proc. R. Soc. London, Ser. A, 82(557), pp. 546–559.

[CrossRef]Poynting, J. H., 1912, “On the Changes in the Dimensions of a Steel Wire When Twisted, and on the Pressure of Distortional Waves in Steel,” Proc. R. Soc. London, Ser. A, 86(590), pp. 534–561.

[CrossRef]Foux, A., 1964, “An Experimental Investigation of the Poynting Effect,” International Symposium on the Second-Order Effects in Elasticity, Plasticity and Fluid Dynamics, Haifa, Israel, Apr. 23–27, pp. 228–251.

Billington, E. W., 1977, “Non-Linear Mechanical Response of Various Metals. I. Dynamic and Static Response to Simple Compression, Tension and Torsion in the As-Received and Annealed States,” J. Phys. D: Appl. Phys., 10(4), pp. 519–531.

[CrossRef]Billington, E. W., 1986, “The Poynting Effect,” Acta Mech., 58(1–2), pp. 19–31.

[CrossRef]Wack, B., 1989, “The Torsion of a Tube (or a Rod): General Cylindrical Kinematics and Some Axial Deformation and Ratchet Measurements,” Acta Mech., 80(1–2), pp. 39–59.

[CrossRef]Freudenthal, A. M., and Ronay, M., 1966, “Second Order Effects in Dissipative Media,” Proc. R. Soc. London, Ser. A, 292(1428), pp. 14–50.

[CrossRef]Rivlin, R. S., and Saunders, D., 1951, “Large Elastic Deformations of Isotropic Materials. VII. Experiments on the Deformation of Rubber,” Philos. Trans. R. Soc., A, 243(865), pp. 251–288.

[CrossRef]Mooney, M., 1940, “A Theory of Large Elastic Deformation,” J. Appl. Phys., 11(9), pp. 582–592.

[CrossRef]Shield, R. T., 1980, “An Energy Method for Certain Second-Order Effects With Application to Torsion of Elastic Bars Under Tension,” ASME J. Appl. Mech., 47(1), pp. 75–81.

[CrossRef]Jiang, X., and Ogden, R. W., 2000, “Some New Solutions for the Axial Shear of a Circular Cylindrical Tube of Compressible Elastic Material,” Int. J. Non Linear Mech., 35(2), pp. 361–369.

[CrossRef]Brigadnov, I. A., 2015, “Power Law Type Poynting Effect and Non-Homogeneous Radial Deformation in the Boundary-Value Problem of Torsion of a Nonlinear Elastic Cylinder,” Acta Mech., 226(4), pp. 1309–1317.

[CrossRef]Anand, L., 1979, “On H. Hencky's Approximate Strain-Energy Function for Moderate Deformations,” ASME J. Appl. Mech., 46(1), pp. 78–82.

[CrossRef]Anand, L., 1986, “Moderate Deformations in Extension-Torsion of Incompressible Isotropic Elastic Materials,” J. Mech. Phys. Solids, 34(3), pp. 293–304.

[CrossRef]Horgan, C. O., and Murphy, J. G., 2009, “A Generalization of Hencky's Strain-Energy Density to Model the Large Deformations of Slightly Compressible Solid Rubbers,” Mech. Mater., 41(8), pp. 943–950.

[CrossRef]Bruhns, O. T., Xiao, H., and Meyers, A., 2000, “Hencky's Elasticity Model With the Logarithmic Strain Measure: A Study on Poynting Effect and Stress Response in Torsion of Tubes and Rods,” Arch. Mech., 52(4–5), pp. 489–509.

Storm, C., Pastore, J. J., MacKintosh, F. C., Lubensky, T. C., and Janmey, P. A., 2005, “Nonlinear Elasticity in Biological Gels,” Nature, 435(7039), pp. 191–194.

[CrossRef] [PubMed]Janmey, P. A., McCormick, M. E., Rammensee, S., Leight, J. L., Georges, P. C., and MacKintosh, F. C., 2007, “Negative Normal Stress in Semiflexible Biopolymer Gels,” Nat. Mater., 6(1), pp. 48–51.

[CrossRef] [PubMed]Zubov, L. M., 2001, “Direct and Inverse Poynting Effects in Elastic Cylinders,” Dokl. Phys., 46(9), pp. 675–677.

[CrossRef]Mihai, L. A., and Goriely, A., 2011, “Positive or Negative Poynting Effect? The Role of Adscititious Inequalities in Hyperelastic Materials,” Proc. R. Soc. A, 467(2136), pp. 3633–3646.

[CrossRef]Mihai, L. A., and Goriely, A., 2013, “Numerical Simulation of Shear and the Poynting Effects by the Finite Element Method: An Application of the Generalised Empirical Inequalities in Non-Linear Elasticity,” Int. J. Non Linear Mech., 49, pp. 1–14.

[CrossRef]Wang, D., and Wu, M. S., 2014, “Poynting and Axial Force–Twist Effects in Nonlinear Elastic Mono- and Bi-Layered Cylinders: Torsion, Axial and Combined Loadings,” Int. J. Solids Struct., 51(5), pp. 1003–1019.

[CrossRef]Kanner, L. M., and Horgan, C. O., 2008, “On Extension and Torsion of Strain-Stiffening Rubber-Like Elastic Circular Cylinders,” J. Elasticity, 93(1), pp. 39–61.

[CrossRef]Horgan, C. O., and Murphy, J. G., 2012, “Finite Extension and Torsion of Fiber-Reinforced Non-Linearly Elastic Circular Cylinders,” Int. J. Non Linear Mech., 47(2), pp. 97–104.

[CrossRef]Wu, M. S., and Wang, D., 2015, “Nonlinear Effects in Composite Cylinders: Relations and Dependence on Inhomogeneities,” Int. J. Eng. Sci., 90, pp. 27–43.

[CrossRef]Berdichevsky, V. L., 2009, *Variational Principles of Continuum Mechanics: I. Fundamentals*, 1st ed., Springer-Verlag, La Vergne, TN, pp. 243–269.

Yu, W., Hodges, D. H., and Ho, J. C., 2012, “Variational Asymptotic Beam Sectional Analysis—An Updated Version,” Int. J. Eng. Sci., 59, pp. 40–64.

[CrossRef]Danielson, D. A., and Hodges, D. H., 1987, “Nonlinear Beam Kinematics by Decomposition of the Rotation Tensor,” ASME J. Appl. Mech., 54(2), pp. 258–262.

[CrossRef]Hodges, D. H., 1999, “Non-Linear Inplane Deformation and Buckling of Rings and High Arches,” Int. J. Non Linear Mech., 34(4), pp. 723–737.

[CrossRef]Hodges, D. H., 1990, “A Mixed Variational Formulation Based on Exact Intrinsic Equations for Dynamics of Moving Beams,” Int. J. Solids Struct., 26(11), pp. 1253–1273.

[CrossRef]Hodges, D. H., Atilgan, A. R., Cesnik, C. E. S., and Fulton, M. V., 1992, “On a Simplified Strain Energy Function for Geometrically Nonlinear Behaviour of Anisotropic Beams,” Compos. Eng., 2(5), pp. 513–526.

[CrossRef]Popescu, B., and Hodges, D. H., 2000, “On Asymptotically Correct Timoshenko-Like Anisotropic Beam Theory,” Int. J. Solids Struct., 37(3), pp. 535–558.

[CrossRef]Yu, W., and Hodges, D. H., 2004, “Elasticity Solutions Versus Asymptotic Sectional Analysis of Homogeneous, Isotropic, Prismatic Beams,” ASME J. Appl. Mech., 71(1), pp. 15–23.

[CrossRef]Yu, W., Hodges, D. H., Volovoi, V., and Cesnik, C. E. S., 2002, “On Timoshenko-Like Modeling of Initially Curved and Twisted Composite Beams,” Int. J. Solids Struct., 39(19), pp. 5101–5121.

[CrossRef]Yu, W., Volovoi, V. V., Hodges, D. H., and Hong, X., 2002, “Validation of the Variational Asymptotic Beam Sectional Analysis,” AIAA J., 40(10), pp. 2105–2112.

[CrossRef]Degener, M., Hodges, D. H., and Petersen, D., 1988, “Analytical and Experimental Study of Beam Torsional Stiffness With Large Axial Elongation,” ASME J. Appl. Mech., 55(1), pp. 171–178.

[CrossRef]Sicard, J. F., and Sirohi, J., 2014, “An Analytical Investigation of the Trapeze Effect Acting on a Thin Flexible Ribbon,” ASME J. Appl. Mech., 81(12), p. 121007.

[CrossRef]