[1] Abbassi, M. M., Torsion of circular shafts of variable diameter, ASME J. Appl. Mech., 22, 530–532, 1955.
[2] Abeyaratne, R. and C. O., Horgan, The pressurized hollow sphere problem in finite elastostatics for a class of compressible materials, Int. J. Solids Struct., 20(8), 715–723, 1984.
[3] Acharya, A., On compatibility conditions for the left Cauchy–Green deformation field in three dimensions, J. Elasticity, 56(2), 95–105, 1999.
[4] Ahmad, F. and M. A., Rashid, Linear invariants of a Cartesian tensor, Quart. J. Mech. Appl. Math., 62(1), 31–38, 2009.
[5] Anand, L., On H. Hencky's approximate strain energy function for moderate deformations, ASME J. Appl. Mech., 46(1), 78–82, 1979.
[6] Anand, L., Moderate deformations in extension-torsion of incompressible isotropic elastic materials, J. Mech. Phys. Solids, 34(3), 293–304, 1986.
[7] Anderson, G. L. and C. R., Thomas, A forced vibration problem involving time derivatives in the boundary conditions, J. Sound Vibrat., 14(2), 193–214, 1971.
[8] Andrews, D. L. and W. A., Ghoul, Irreducible fourth-rank Cartesian tensors, Phys. Rev. A, 25(5), 2647–2657, 1982.
[9] Andrianov, I. V. and J., Awrejcewicz, Compatibility equations in the theory of elasticity, J. Vibrat. Acoustics 125(2), 244–245, 2003.
[10] Angel, Y. C., On the static and dynamic equilibrium of concentrated loads in linear acoustics and linear elasticity, J. Elast., 24(1–3), 21–42, 1990.
[11] Antman, S. S. and J. E., Osborn, The principle of virtual work and the integral laws of motion, Arch. Rational Mech. Anal., 69(3), 231–, 1979.
[12] Armero, F., Elastoplastic and viscoplastic deformations in solids and structures, Encyclopedia of Computational Mechanics, Vol. II: Solids and Structures, Eds. E., Stein, Rene, Borst and T. J. R., Hughes, 227–266, 2004.
[13] Ball, J. M. and D. G., Schaeffer, Bifurcation and stability of homogeneous equilibrium configurations of an elastic body under dead-load tractions, Math. Proc. Camb. Phil. Soc., 94(02), 315–339, 1983.
[14] Bakker, M. C. M., M. D, Verweij, B. J., Kooij, H. A., Dieterman, The traveling point load revisited, Wave Motion, 29(2), 119–135, 1999.
[15] Batista, M., Stresses in a confocal elliptic ring subject to uniform pressure, J. Strain Anal., 34(3), 217–221, 1999.
[16] Bauer, H. F., Table of the roots of the associated Legendre function with respect to the degree, Math. Comput., 46(174), 601–602/S29–S41, 1986.
[17] Beatty, M. F., Topics in finite elasticity: hyperelasticity of rubber, elastomers, and biological tissues–with examples, Appl. Mech. Rev., 40(12), 1699–1734, 1987.
[18] Belik, P. and R., Fosdick, The state of pure shear, J. Elast., 52, 91–98, 1998.
[19] Bertram, A. and B., Svendsen, On material objectivity and reduced constitutive equations, Arch. Mech., 53(6), 653–675, 2001.
[20] Betten, J., Mathematical modelling of materials behavior under creep conditions, Appl. Mech. Reviews., 54(2), 107–132, 2001.
[21] Bischoff, J. E., E. M., Arruda and K., Grosh, A new constitutive model for the compressibility of elastomers at finite deformations, Rubber Chem. Tech., 74(4), 541–559, 2001.
[22] Blackmore, D. and L., Ting, Surface integral of its mean curvature vector, SIAM Rev., 27(4), 569–572, 1985.
[23] Blume, J., Compatibility conditions for a left Cauchy–Green strain field, J. Elast., 21(3), 271–308, 1989.
[24] de Boor, C., A naive proof of the representation theorem for isotropic, linear asymmetric stress–strain relations, J. Elast., 15(2), 225–227, 1985.
[25] Borodachev, N. M., Three-dimensional elasticity-theory problem in terms of the stress, Int. Appl. Mech., 31(12), 991–996, 1995.
[26] Bosch, A. J., The factorization of a square matrix into two symmetric matrices. Am. Math. Monthly, 93(6), 462–464, 1986.
[27] Bounlanger, P. and M., Hayes, On pure shear, J. Elast., 77(1), 83–89, 2004.
[28] Bradley, F. E., Development of an Airy stress function of general applicability in one, two, or three dimensions, J. Appl. Phys., 67(1), 225–226, 1990.
[29] Bramble, J. H., The thick elastic spherical shell under concentrated torques, Proc. London Math. Soc., s3–9(4), 492–502, 1959.
[30] Brown, D. K., A computer program to calculate the elastic stress and displacement fields around an elliptical hole under any applied plane state of stress, Comput. Struct., 7(4), 571–580, 1977.
[31] Bruhns, O. T., H, Xiao and A., Meyers, Constitutive inequalities for an isotropic elastic strain-energy function based on Hencky's logarithmic strain tensor, Proc. R. Soc. London Ser. A, 457(2013), 2207–2226, 2001.
[32] Bruhns, O. T., H, Xiao and A., Meyers, Finite bending of a rectangular block of an elastic Hencky material, J. Elast., 66(3), 237–256, 2002.
[33] Bustamante, R., Some topics on a new class of elastic bodies, Proc. R. Soc. Ser. A, 465(2105), 1377–1392, 2009.
[34] Cardoso, J. R., An explicit formula for the matrix logarithm, S. Afr. Optom., 64(3), 80–83, 2005.
[35] Carlson, D. E., Unpublished notes on continuum mechanics. Available at http://imechanica.org/node/15845 (courtesy of Professor Amit Acharya).
[36] Carlson, D. E., Linear thermoelasticity, Handbuch der Physik, Vol. VIa/2., Berlin Heidelberg: Springer-Verlag, 297–345, 1972.
[37] Carlson, D. E. and A., Hoger, The derivative of a tensor-valued function of a tensor, Quart. Appl. Math., 44(3), 409–423, 1986.
[38] Carlson, D. E. and A., Hoger, On the derivatives of the principal invariants of a second-order tensor, J. Elast., 16(2), 221–224, 1986.
[39] Carlson, D. E., E., Fried and D. A., Tortorelli, Geometrically-based consequences of internal constraints, J. Elast., 70(1–3), 101–109, 2003.
[40] Carroll, M. M., Finite strain solutions in compressible isotropic elasticity, J. Elast., 20(1), 65–92, 1988.
[41] Carroll, M. M. and C. O., Horgan, Finite strain solutions for a compressible elastic solid, Q. Appl. Math., 48(4), 767–780, 1990.
[42] Chadwick, P., Thermo-mechanics of rubberlike materials, Phil. Trans. R. Soc. London Ser. A., 276(1260), 371–403, 1974.
[43] Chadwick, P., Continuum Mechanics, New York: Dover Publications, 1976.
[44] Chattarji, P. P., Torsion of epitrochoidal sections, Z. Angew Math. Mech., 89(3/4), 135–138, 1959.
[45] Chattarji, P. P., A note on the torsion of circular shafts of variable diameter, ASME J. Appl. Mech., 29, 477–478, 1957.
[46] Chen, Y. C., Stability of homogeneous deformations of an incompressible elastic body under dead-load surface tractions, J. Elast., 17(3), 223–248, 1987.
[47] Chen, Y. and L., Wheeler, Derivatives of the stretch and rotation tensors, J. Elast., 32(3), 1757ndash;182, 1993.
[48] Chen, S. J. and D. G., Howitt, On the Galerkin vector and the Eshelby solution in linear elasticity, J. Elast., 44(1), 1–8, 1996.
[49] Chen, T., A homogeneous elliptical shaft may not warp under torsion, Acta Mech., 169(1–4), 221–224, 2004.
[50] Chen, T. and C. J., Wei, Saint-Venant torsion of anisotropic shafts: Theoretical frameworks, extremal bounds and affine transformations, Quart. J. Mech. Appl. Math., 58(2), 269–287, 2005.
[51] Cheng, S. and T., Angsirikul, Three-dimensional elasticity solution and edge effects in a spherical dome, ASME J. Appl. Mech., 44(4), 599–603, 1977.
[52] Cheng, H-W. and S., Yau, More explicit formulas for the matrix exponential, Lin. Alg. Appl., 262, 131–163, 1997.
[53] Cheng, S. H., N. J., Higham, C. S., Kenney and A. L., Laub, Approximating the logarithm of a matrix to specified accuracy, SIAM J. Matrix Anal. Appl., 22(4), 1112–1125, 2001.
[54] Chiang, C-R., Torsion of a round shaft of variable diameter, J. Eng. Math., 77(1), 119–130, 2012.
[55] Chree, C., On long rotating circular cylinders, Proc. Cambridge Philos. Soc., 7, 283–305, 1892.
[56] Christov, C. I., On frame indifferent formulation of the Maxwell-Cattaneo model of finite-speed heat conduction, Mech. Res. Commun., 36(4), 481–486, 2009.
[57] Chung, D. T., C. O., Horgan and R., Abeyaratne, The finite deformation of internally pressurized hollow cylinders and spheres for a class of compressible materials, Int. J. Solids Struct., 22(12), 1557–1570, 1986.
[58] Ciarlet, P. G., Three-Dimensional Elasticity, Elsevier Science Publishers, North Holland, 1988.
[59] Ciarlet, P. G., An introduction to differential geometry with applications to elasticity, J. Elast., 78–79(1–3), 1–215, 2005.
[60] Ciarlet, P. G., On rigid and infinitesimal rigid displacements in three-dimensional elasticity, Math. Models Meth. Appl. Sci., 13(11), 1589–1598, 2003.
[61] Coleman, B. D. and W., Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal., 13(1), 245–261, 1963.
[62] Coleman, B. D. and V. J., Mizel, Existence of caloric equations of state in thermodynamics, J. Chem. Phys., 40(4), 1116–1125, 1964.
[63] Conway, J. B., A Course in Functional Analysis, Springer, New York, 1990.
[64] Dai, H. H., Model equations for nonlinear dispersive waves in a compressible Mooney–Rivlin rod, Acta Mech., 127(1–4), 193–207, 1998.
[65] Dempsey, J. P., The wedge subjected to tractions: a paradox resolved, J. Elast., 11(1), 1–10, 1981.
[66] Donnell, L. H., Stress concentrations due to elliptical discontinuities in plates under edge force, Theodore von Karman Anniversary Volume, California Institute of Technology, Pasadena, 293–309, 1941.
[67] Dui, G., M., Jin and M., Huang, On the derivation for the gradients of the principal invariants, J. Elast., 75(2), 193–196, 2004.
[68] Dui, G. and Y., Chen, A note on Rivlin's identities and their extension, J. Elast., 76(2), 107–112, 2004.
[69] Edstrom, C. R., The vibrating beam with nonhomogeneous boundary conditions, ASME J. Appl. Mech., 48(3), 669–670, 1981.
[70] Edwards, R. H., Stress concentrations around spheroidal inclusions and cavities, ASME J. Appl. Mech., 18(1), 19–30, 1951.
[71] Ehlers, W. and G., Eipper, The simple tension problem at large volumetric strains computed from finite hyperelastic material laws, Acta Mech., 130(1–2), 17–27, 1998.
[72] Ericksen, J. L., Deformations possible in every compressible, isotropic, perfectly elastic material, J. Math. Phys., 34(2), 126–128, 1955.
[73] Ericksen, J. L., Equilibrium theory of liquid crystals, Advances in Liquid crystals, Vol. 2, Ed. G. H., Brown, pp. 233–298, Academic Press, New York, 1976.
[74] Eshelby, J. B., The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. R. Soc. London Ser. A, 241(1226), 376–396, 1957.
[75] Eskin, G. and J., Ralston, On the inverse boundary value problem for linear isotropic elasticity, Inverse Problems, 18(3), 907–921, 2002.
[76] Filon, L. N. G., On the elastic equilibrium of circular cylinders under certain practical systems of load, Phil. Trans. R. Soc. of London Ser. A., 198, 147–233, 1902.
[77] Filon, L. N. G., On an approximate solution for the bending of a beam of rectangular cross-section under any system of load, with special reference to points of concentrated or discontinuous loading, Phil. Trans. R. Soc. London Ser. A., 201, 63–155, 1903.
[78] Fish, M. J., A particular boundary value problem, J. Math. Phys., 14, 262–273, 1935.
[79] Fisher, H. D., Discussion on [?], ASME J. Appl. Mech., 49(2), 459–460, 1982.
[80] Folias, E. S. and J. J., Wang, On the three-dimensional stress field around a circular hole in a plate of arbitrary thickness, Comput. Mech., 6(5–6), 379–391, 1990.
[81] Fosdick, R. and G., Royer-Carfagni, The constraint of local injectivity in linear elasticity theory, Proc. R. Soc. London Ser. A, 457(2013), 2167–2187, 2001.
[82] Fosdick, R., F., Freddi and G., Royer-Carfagni, Bifurcation instability in linear elasticity with the constraint of local injectivity, J. Elast., 90(1), 99–126, 2008.
[83] Freddi, F. and G., Royer-Carfagni, From non-linear elasticity to linearized theory: Examples defying intuition, J. Elast., 96(1), 1–26, 2009.
[84] Freiberger, W., The uniform torsion of an incomplete tore, Austral. J. Sci. Res. Ser. A, 2(3), 354–375, 1949.
[85] Fulmer, E. P., Computation of the matrix exponential, Am. Math. Monthly, 82(2), 156–159, 1975.
[86] Gallier, J. and D., Xu, Computing of exponentials of skew-symmetric matrices and logarithms of orthogonal matrices, Int. J. Robotics Auto., 17(4), 1–11, 2002.
[87] Gao, X. L., A general solution of an infinite elastic plate with an elliptic hole under biaxial loading, Int. J. Pres. Ves. Piping, 67(1), 95–104, 1996.
[88] Galmudi, D. and J., Dvorkin, Stresses in anisotropic cylinders, Mech. Res. Comm., 22(2), 109–113, 1995.
[89] Georgiadis, H. G., D., Vamvatsikos, I., Vardoulakis, Numerical implementation of the integral-transform solution to Lamb's point-load problem, Comput. Mech., 24(2), 90–99, 1999.
[90] Gerhardt, T. O., and S., Cheng, Truncated hollow spheres, ASCE J. Eng. Mech., 109(3), 885–895, 1983.
[91] Geymonat, G. and F., Krasucki, Beltrami's solutions of general equilibrium equations in continuum mechanics, C. R. Acad. Sci. Paris, Ser I, 342(5), 359–363, 2006.
[92] Ghosh, A. K., Axisymmetric vibration of a long cylinder, J. Sound Vibrat., 186(5), 711–721, 1995.
[93] Goldberg, M. A. and M., Sadowsky, Stresses in an ellipsoidal rotor in a centrifugal force field, J. Appl. Mech., 26(4), 549–552, 1959.
[94] Goldberg, M. A., V. L., Salerno and M. A., Sadowsky, Stress distribution in a rotating spherical shell of arbitrary thickness, J. Appl. Mech., 28(1), 127–131, 1961.
[95] Golovchan, V. T., Torsion of a cylinder of finite length having a cylindrical cavity, Prikladnaya Mekhanika, 8(3), 37–41, 1972.
[96] Gong, S. X. and S. A., Meguid, On the elastic fields of an elliptical inhomogeneity under plane deformation, Proc. R. Soc. London Ser. A, 443(1919), 457–471, 1993.
[97] Goodier, J. N., Concentration of stress around spherical and cylindrical inclusions and flaws, Trans. ASME, Applied Mech., 55(7), 39–44, 1933.
[98] Goss, R. N., Center of flexure of a triangular beam, Proc. Am. Math. Soc., 1(6), 744–750, 1950.
[99] Grant, D. A., Beam vibrations with time-dependent boundary conditions, J. Sound Vibrat., 89(4), 519–522, 1983.
[100] Green, A. E., Three-dimensional stress systems in isotropic plates. I, Phil. Trans. R. Soc. London Ser. A, 240(825), 561–597, 1948.
[101] Gregory, R., D. and I., Gladwell, The cantilever beam under tension, bending or flexure at infinity, J. Elast., 12(4), 317–343, 1982.
[102] Guo, Z. H., The representation theorem for isotropic, linear asymmetric stress–strain relations, J. Elast., 13(2), 121–124, 1983.
[103] Guo, Z. H., An alternative proof of the representation theorem for isotropic, linear asymmetric stress–strain relations, Quart. Appl. Math., 41(1), 119–123, 1983.
[104] Guo, Z. H., Rates of stretch tensors, J. Elast., 14(3), 263–267, 1984.
[105] Guo, Z. H. and P., Podio–Guidugli, A concise proof of the representation theorem for linear isotropic, tensor-valued mappings of a skew argument, J. Elast., 21(3), 317–320, 1989.
[106] Guo, Z. H., Derivatives of the principal invariants of a 2-nd order tensor, J. Elast., 22(2), 185–191, 1989.
[107] Gupta, A., D. J., Steigmann and J. S., Stolken, On the evolution of plasticity and incompatibility, Math. Mech. Solids, 12(6), 583–610, 2007.
[108] Gurtin, M. E., An Introduction to Continuum Mechanics, San Diego:Academic Press, 1981.
[109] Gurtin, M. E., The Linear Theory of Elasticity, Handbuch der Physik VIa/2, Berlin Heidelberg:Springer-Verlag, 1972.
[110] Gurtin, M. E., A short proof of the representation theorem for isotropic, linear stress–strain relations, J. Elast., 4(3), 243–245, 1974.
[111] Gurtin, M. E., A generalization of Beltrami stress functions in continuum mechanics, Arch. Rational Mech. Anal., 13(1), 321–329, 1963.
[112] Gurtin, M. E. and L., Anand, The decomposition F = FeFp, material symmetry, and plastic irrotationality for solids that are isotropic-viscoplastic or amorphous, Int. J. Plast., 21(9), 1686–1719, 2005.
[113] Hadjesfandiari, A. R. and G. F., Dargush, Analysis of bi-material interface cracks with complex weighting functions and non-standar quadrature, Int. J. Solids Struct., 48(10), 1499–1512, 2011.
[114] Hardiman, N. J., Elliptic elastic inclusion in an infinite elastic plate, Quart. J. Mech Appl. Math., 7(2), 226–230, 1954.
[115] Hartmann, S. and P., Neff, Polyconvexity of generalized polynomial-type hyperelastic strain energy function for near-incompressibility, Int. J. Solids Struct., 40(11), 2767–2791, 2003.
[116] Hay, G. E., The method of images applied to the problem of torsion, Proc. London Math. Soc., s2–45(1), 382–397, 1939.
[117] Hayes, M. and T. J., Laffey, Pure shear–A footnote, J. Elast., 92(1), 109–113, 2008.
[118] Higgins, T. J., A comprehensive review of Saint-Venant's torsion problem, Am J. Phys., 10(5), 248–259, 1942.
[119] Higgins, T. J., Stress analysis of shafting exemplified by Saint Venant's torsion problem, Experimental Stress Analysis, 3(1), 94–101, 1945.
[120] Hill, R., On uniqueness and stability in the theory of finite elastic strain, J. Mech. Phys. Solids, 5(4), 229–241, 1957.
[121] Hill, R., Constitutive inequalities for isotropic elastic solids under finite strain, Proc. R. Soc. London Ser. A, 314(1519), 457–472, 1970.
[122] Hill, J. M. and J. N., Dewynne, Heat Conduction, Boston: Blackwell Scientific Publications, 1987.
[123] Hillman, A. P. and H. E., Salzer, Roots of sin z = z. Phil. Mag., 34 (235), 575–575, 1943.
[124] Hiramatsu, Y. and Y., Oka, Determination of the tensile strength of rock by a compression test of an irregular test piece, Int. J. Rock Mech. Min. Sci., 3(2), 89–99, 1966.
[125] Hoffman, K. M. and R., Kunze, Linear Algebra, New Jersey: Prentice Hall, 1971.
[126] Hoger, A. and D. E., Carlson, Determination of the stretch and rotation in the polar decomposition of the deformation gradient, Quart. Appl. Math., 42(1), 113–117, 1984.
[127] Hoger, A. and D. E., Carlson, On the derivative of the square root of a tensor and Guo's rate theorems, J. Elast., 14(3), 329–336, 1984.
[128] Hoger, A., The stress conjugate to logarithmic strain, Int. J. Solids Struct., 23(12), 1645–1656, 1987.
[129] Holl, D. L. and D. H., Rock, The flexure and torsion of a beam whose cross-section is a limacon, Z. Angew Math. Mech., 19(3), 141–145, 1939.
[130] Holzapfel, G. A. and J. C., Simo, Entropy elasticity of isotropic rubber–like solids at finite strains, Comput. Methods Appl. Mech. Eng., 132(1), 17–44, 1996.
[131] Horgan, C. O. and S. C., Baxter, Effects of curvilinear anisotropy on radially symmetric stresses in anisotropic linearly elastic solids, J. Elast., 42(1), 31–48, 1996.
[132] Horgan, C. O., Equilibrium solutions for compressible nonlinearly elastic materials. In: Y. B., Fu and R. W., Ogden, Eds., Nonlinear elasticity: Theory and applications, Cambridge: Cambridge University Press, 2001.
[133] Horgan, C. O., On the torsion of functionally graded anisotropic linearly elastic bars, IMA J. Appl. Math., 72(5), 556–562, 2007.
[134] Horgan, C. O. and J. G., Murphy, A generalization of Hencky's strain-energy density to model the large deformations of slightly compressible solid rubbers, Mech. Mater., 41(8), 943–950, 2009.
[135] Horibe, T., E., Tsuchida, Y., Arai and N., Kusano, Stresses in an elastic strip having a circular inclusion under tension, J. Solid Mech. Mater. Eng., 2(7), 900–911, 2008.
[136] Horn, R. A. and C. R., Johnson, Topics in Matrix Analysis, Cambridge: Cambridge University Press, 1991.
[137] Huber, A., The elastic sphere under concentrated torques, Quart. Appl. Math., 13(1), 98–102, 1955.
[138] Hunter, S. C., Mechanics of Continuous Media, Chichester: Ellis Horwood Limited, 1983.
[139] Inglis, C. E., Stresses in a plate due to the presence of cracks and sharp corners, Trans. Institution of Naval Architects, 60, 219–230, 1913.
[140] Iyengar, K. T. and M. K., Prabhakara, A three-dimensional elasticity solution for rectangular prism under end loads, Z. Angew Math. Mech., 49(6), 321–332, 1969.
[141] Itskov, M., On the theory of fourth-order tensors and their applications in computational mechanics, Comp. Meth. Appl. Mech. Eng., 189(2), 419–438, 2000.
[142] Itskov, M., The derivative with respect to a tensor: Some theoretical aspects and applications, Z. Angew Math. Mech., 82(8), 535–544, 2002.
[143] Itskov, M. and N., Aksel, A closed-form representation for the derivative of non-symmetric tensor power series, Int. J. Solids Struct., 39, 5963–5978, 2002.
[144] Itskov, M., Application of the Dunford-Taylor integral to isotropic tensor functions and their derivatives, Proc. R. Soc. London Ser. A, 459(2034), 1449–1457, 2003.
[145] Jain, R., K., Ramachandra and K. R. Y., Simha, Rotating anisotropic disc of uniform strength, Int. J. Mech. Sci., 41(6), 639–648, 1999.
[146] Jain, R., K., Ramachandra and K. R. Y., Simha, Singularity in rotating orthotropic discs and shells, Int. J. Solids Struct., 37(14), 2035–2058, 2000.
[147] Jaric, J. P., On the gradients of the principal invariants of a second-order tensor, J. Elast., 44(3), 285–287, 1996.
[148] Jaric, J. P., On the representation of symmetric isotropic 4-tensors, J. Elast., 51(1), 73–79, 1998.
[149] Jeffrey, G. B., Plane stress and plane strain in bipolar co-ordinates, Phil. Trans. R. Soc. London Ser. A., 221, 265–293, 1921.
[150] Jerphagnon, J., Invariants of the third-rank Cartesian tensor: Optical nonlinear susceptibilities, Phys. Rev. B, 2(4), 1091–1098, 1970.
[151] Jerphagnon, J., D., Chemla and R., Bonneville, The description of the physical properties of condensed matter using irreducible tensors, Adv. Phys., 27(4), 609–650, 1978.
[152] Jiang, X. and R. W., Ogden, On azimuthal shear of a circular cylindrical tube of compressible elastic material, Q. J. Mech. Appl. Math., 51(1), 143–158, 1998.
[153] Jog, C. S., On the explicit determination of the polar decomposition in n-dimensional vector spaces, J. Elast., 66(2), 159–169, 2002.
[154] Jog, C. S., The accurate inversion of Vandermonde matrices, Comput. Math. Appl., 47(6–7), 921–929, 2004.
[155] Jog, C. S., Derivatives of the stretch, rotation and exponential tensors in n-dimensional vector spaces, J., Elast., 82(2), 175–192, 2006.
[156] Jog, C. S. and P. P., Kelkar, Nonlinear analysis of structures using high performance hybrid elements, Int. J. Num. Meth. Eng., 68(4), 473–501, 2006.
[157] Jog, C. S., A concise proof of the representation theorem for fourth-order isotropic tensors, J. Elast., 85(2), 119–124, 2006.
[158] Jog, C. S., The explicit determination of the logarithm of a tensor and its derivatives, J. Elast., 93(2), 141–148, 2008.
[159] Jog, C. S. and R., Bayadi, Stress and strain-driven algorithmic formulations for finite strain viscoplasticity for hybrid and standard finite elements, Int. J. Num. Meth. Eng., 79(7), 773–816, 2009.
[160] Jog, C. S. and Phani, Motammari, An energy-momentum conserving algorithm for nonlinear transient analysis within the framework of hybrid elements, J. Mech. Materials Struct., 4(1), 157–186, 2009.
[161] Jog, C. S., Improved hybrid elements for structural analysis, J. Mech. Materials Struct., 5(3), 507–528, 2010.
[162] Jog, C. S. and R. K., Pal, A monolithic strategy for fluid-structure interaction problems, Int. J. Num. Meth. Eng., 85(4), 429–460, 2011.
[163] Jog, C. S., The equations of equilibrium in orthogonal curvilinear reference coordinates, J. Elast., 104(1), 385–395, 2011.
[164] Jog, C. S. and K. D., Patil, Conditions for the onset of elastic and material instabilities in hyperelastic materials, Arch. Mech., 83(5), 661–684, 2013.
[165] Jog, C. S. and H. P., Cherukuri, A reexamination of some puzzling results in linearized elasticity, Sadhana, 39(1), 137–147, 2014.
[166] Jog, C. S. and I. S., Mokashi, A finite element method for the Saint-Venant torsion and bending problems for prismatic beams, Comput. Struct., 135, 62–72, 2014.
[167] Jog, C. S. and A., Nandy, Conservation properties of the trapezoidal rule in linear time domain analysis of acoustics and structures, ASME J. Vibration Acoustics, 137(2), 021010, 2015.
[168] Johnson, C., Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge: Cambridge University Press, 1990.
[169] Jones, D. L. and C. P., Burke, Zonal harmonic series expansions of Legendre functions and associated Legendre functions, J. Phys. A, 23(14), 3159–3168, 1990.
[170] Kalman, D., A Matrix Proof of Newton's Identities, Math. Mag., 73(4), 313–315, 2000.
[171] Kantorovich, L. V. and V. I., Krylov, Approximate Methods of Higher Analysis, Groningen:P. Noordhoff Limited, 1958.
[172] Kawashima, K., E., Tsuchida and I., Nakahara, Stresses in an elastic circular cylinder having a spherical inclusion under tension, Theo. Appl. Mech., 27, 79–89, 1979.
[173] Kearsly, E. A., Asymmetric stretching of a symmetrically loaded elastic sheet. J. Elast., 22(2), 111–119, 1986.
[174] Knowles, J. K. and E., Sternberg, On the ellipticity of the equations of nonlinear elastostatics for a special material, J. Elast., 5(3–4), 341–361, 1975.
[175] Knowles, J. K., On the representation of the elasticity tensor for isotropic materials, J. Elast., 39(2), 175–180, 1995.
[176] Knowles, J. K., Linear Vector Spaces and Cartesian Tensors, New York: Oxford University Press, 1998.
[177] Kolossoff, M. C., Sur la torsion des primes ayant pour base un triangle rectangle, Comptes Rendus, 178, 2057–2060, 1924.
[178] Kondo, M., Eine methode zur losung der drehungsspannungen der walztrager von den rechtwinkligen und gleichschenkligen dreieck-formigen querschnitten, J. Jap. Soc. Mech. Eng., 36(194), 408–416, 1933.
[179] Korsgaard, J., On the representation of symmetric tensor-valued isotropic functions, Int. J. Eng. Sci., 28(12), 1331–1346, 1990.
[180] Krawietz, A., A comprehensive constitutive inequality in finite elastic strain, Arch. Rational Mech. Anal., 58(2), 127–149, 1975.
[181] Kutsenko, G. V. and A. F., Ulitko, Elastic equilibrium of an ellipsoid under the influence of concentrated forces, Int. Appl. Mech., 9(4), 359–364, 1973.
[182] Kutsenko, G. V. and A. F., Ulitko, An exact solution of the axisymmetric problem of the theory of elasticity for a hollow ellipsoid of revolution, Int. Appl. Mech., 11(10), 1029–1032, 1975.
[183] Langhaar, H. L., Torsion of curved beams of rectangular cross-section, ASME J. Appl. Mech., 19(1), 49–53, 1952.
[184] Lekhnitskii, S. G., Anisotropic plates, New York: Gordon Breach, 1968.
[185] Leslie, F. M., Some constitutive equations for liquid crystals, Arch. Rational Mech. Anal., 28(4), 265–283, 1968.
[186] Leslie, F. M., Some thermal effects in cholesteric liquid crystals, Proc. R. Soc. London Ser. A., 307(1490), 359–372, 1968.
[187] Leslie, F.M., Theory of flow phenomena in liquid crystals, Advances in Liquid crystals, Vol. 4, Ed. G. H., Brown, pp. 1–81, New York: Academic Press, 1979.
[188] Levine, H.S. and J.M., Klosner, Axisymmetric elasticity solutions of spherical shell segments, ASME J. Appl. Mech., 38(1), 197–208, 1971.
[189] Levinson, M., The simply supported rectangular plate: An exact, three-dimensional, linear elasticity solution, J. Elast., 15(3), 283–291, 1985.
[190] Ling, C.B., On the stresses in a notched plate under tension, J. Math. Phys., 26, 284–289, 1947.
[191] Ling, C.B., K.L., Yang, On symmetrical strain in solids of revolution in spherical coordinates, Trans. J. Appl. Mech., 18(4), 367–370, 1951.
[192] Ling, C.B., Torsion of a circular cylinder having a spherical cavity, Quart. Appl. Math., 10, 149–156, 1952.
[193] Ling, C.B., Stresses in a circular cylinder having a spherical cavity under tension, Quart. Appl. Math., 13(4), 381–391, 1956.
[194] Lion, A., On the large deformation behaviour of reinforced rubber at different temperatures. J. Mech. Phys. Solids, 45(11/12), 1805–1834, 1997.
[195] Little, R.W., Elasticity., New Jersey: Prentice-Hall Inc., 1973.
[196] Little, R.W. and S., B.Childs, Elastostatic boundary region in solid cylinders. Quart. Appl. Math., 25(3), 261–274, 1967.
[197] Liu, I-Shih, Continuum Mechanics, Berlin: Springer-Verlag, 2002.
[198] Liu, I-Shih, On the transformation property of the deformation gradient under a change of frame, J. Elast., 71(1–3), 73–80, 2003.
[199] Liu, I-Shih, On Euclidean objectivity and the principle of material frame-indifference, Continuum Mech. Thermodyn., 16(1–2), 177–183, 2004.
[200] Liu, I-Shih, Further remarks on Euclidean objectivity and the principle of material frame-indifference, Continuum Mech. Thermodyn., 17(2), 125–133, 2005.
[201] Lamb, H., On the propagation of tremors over the surface of an elastic solid, Phil. Trans. R. Soc. London Ser. A., 203, –42, 1904.
[202] Love, A.E.H., The propagation of wave-motion in an isotropic elastic medium, Proc. London Math. Soc., 2(1), 291–344, 1904.
[203] Love, A.E.H., A Treatise on the Mathematical Theory of Elasticity, New York: Dover, 4'th ed., 1927.
[204] Lubarda, V.A., Constitutive theories based on the multiplicative decomposition of deformation gradient: Thermoelasticity, elastoplasticity, and biomechanicsAppl. Mech. Rev., 57(2), 95–108, 2004.
[205] Macdonald, H.M., On the torsional strength of a hollow shaft, Proc. Cambridge Phil. Soc., 8, 62–68, 1893.
[206] MacSithigh, G.P., Energy-minimal finite deformations of a symmetrically loaded elastic sheet, Q. J. Mech. Appl. Math, 39(1), 111–124, 1986.
[207] Malvern, L.E., Introduction to the Mechanics of a Continuous Medium, New Jersey: Prentice Hall Inc., 1969.
[208] Malyi, V.I., One representation of the conditions of the compatibility of deformations, PMM U.S.S.R., 50(5), 679–681, 1986.
[209] Marsden, J.E. and T.J.R., Hughes, Mathematical Foundations of Elast., New York: Dover, 1994.
[210] Martins, L.C. and P., Podio-Guidugli, A new proof of the representation theorem for isotropic, linear constitutive relations, J. Elast., 8(3), 319–322, 1978.
[211] Mathias, R., Evaluating the Frechet derivative of the matrix exponential, Num. Math., 63(1), 213–226, 1992.
[212] Maunsell, F.G., Stresses in a notched plate under tension, Phil. Mag., 21(142), 765–773, 1936.
[213] Mehrabadi, M. M. and S.C., Cowin, Eigentensors of linear anisotropic elastic materials, Quart. J. Mech. Appl. Math., 43(1), 15–41, 1990.
[214] Meleshko, V.V. and A.M., Gomilko, Infinite systems for a biharmonic problem in a rectangle, Proc. R. Soc. London Ser. A, 453(1965), 2139–2160, 1997.
[215] Meleshko, V.V., Equilibrium of an elastic finite cylinder: Filon's problem revisited, J. Engg. Math., 46(3–4), 355–376, 2003.
[216] Meleshko, V.V., Selected topics in the history of the two-dimensional biharmonic problem, Appl. Mech. Rev., 56(1), 33–85, 2003.
[217] Meleshko, V.V., Thermal stresses in an elastic rectangle, J. Elast., 105(1–2), 61–92, 2011.
[218] Merodio, J. and R.W., Ogden, A note on strong ellipticity for transversely isotropic linearly elastic solids, Quart. J. Mech. Appl. Math., 56(4), 589–591, 2003.
[219] Meschke, G. and W.N., Liu, A re-formulation of the exponential algorithm for finite strain plasticity in terms of Cauchy stresses, Comput. Methods Appl. Mech. Eng., 173(1), 167–187, 1999.
[220] Meyers, A., P., Schiebe and O.T., Bruhns, Some comments on objective rates of symmetric Eulerian tensors with application to Eulerian strain rates, Acta Mech., 139(1–4), 91–103, 2000.
[221] Michell, J.H., On the direct determination of stress in an elastic solid, with application to the theory of plates, Proc. London Math. Soc., 1(1), 100–124, 1899.
[222] Michell, J.H., Elementary distributions of plane stress, Proc. London Math. Soc., 32, 35–61, 1900.
[223] Min-zhong, W. and W., Lu-nan, Derivation of some special stress function from Beltrami-Schaefer stress function, Appl. Math. Mech., 10(7), 665–673, 1989.
[224] Mindlin, R.D. and L.E., Goodman, Beam vibrations with time-dependent boundary conditions, ASME J. Appl. Mech., 17(4), 377–380, 1950.
[225] Moler, C. and C.V., Loan, Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later, SIAM Rev., 45(1), 3–49, 2003.
[226] Morinaga, K. and T., Nono, On the non-commutative solutions of the exponential equation exey = ex+y, J. Sci. Hiroshima Univ. (A), 17, 345–358, 1954.
[227] Morinaga, K. and T., Nono, On the non-commutative solutions of the exponential equation exey = ex+y, II, J. Sci. Hiroshima Univ. (A), 18, 137–178, 1954.
[228] Muller, I., On the frame dependence of stress and heat flux, Arch. Rational Mech. Anal., 45(4), 241–250, 1972.
[229] Muller, I., Two instructive instabilities in non-linear elasticity: Biaxially loaded membrane, and rubber balloons, Meccanica, 31(4), 387–395, 1996.
[230] Murdoch, A.I., On objectivity and material symmetry for simple elastic solids, J. Elast., 60(3), 233–242, 2000.
[231] Murdoch, A.I., Objectivity in classical continuum physics: a rationale for discarding the ‘principle of invariance under superposed rigid body motions’ in favor of purely objective considerations, Continuum Mech. Thermodyn., 15(3), 309–320, 2003.
[232] Murdoch, A.I., On criticism of the nature of objectivity in classical continuum physics, Continuum Mech. Thermodyn., 17(2), 135–148, 2005.
[233] Nadeau, J.C. and M., Ferrari, Invariant tensor-to-matrix mappings for evaluation of tensor expressions, J. Elast., 52(1), 43–61, 1998.
[234] Nakamura, G. and G., Uhlmann, Global uniqueness for an inverse boundary value problem arising in elasticity, Inven. Math., 118(1), 457–474, 1994.
[235] Nakamura, G. and G., Uhlmann, Correction to–Global uniqueness for an inverse boundary value problem arising in elasticity, Inven. Math., 152(1), 205–207, 2003.
[236] Noda, N. and Y., Moriyama, Stress concentration of an ellipsoidal inclusion of revolution in a semi-infinite body under biaxial tension, Arch. Appl. Mech., 74(1–2), 29–44, 2004.
[237] Noll, W., The Foundations of Mechanics and Thermodynamics, Berlin: Springer–Verlag, 1974.
[238] Norris, A.N., Quadratic invariants of elastic moduli, Quart. J. Mech. Appl. Math., 60(3), 367–389, 2007.
[239] Ogden, R.W., Large deformation isotropic elasticity: on the correlation of theory and experiment for compressible rubberlike solids, Proc. R. Soc. London Ser. A, 326(1567), 565–584, 1972.
[240] Ogden, R.W., Nonlinear elastic deformations, New York: Dover, 1997.
[241] Ortiz, M.,R.A., Radovitzky and E.A., Repetto, The computation of the exponential and logarithmic mappings and their first and second linearizations, Int. J. Num. Meth. Eng., 52(12), 1431–1441, 2001.
[242] Ostrosablin, N.I., Compatibility conditions of small deformations and stress functions, J. Appl. Mech. Tech. Phys., 38(5), 774–783, 1997.
[243] Ostrosablin, N.I., Comments of the publication “Compatibility conditions of small deformations and stress functions”, J. Appl. Mech. Tech. Phys., 40(3), page 549, 1999.
[244] Padovani, C., On the derivative of some tensor-valued functions, J. Elast., 58(3), 257–268, 2000.
[245] Payne, L. E., Torsion of composite sections, Iowa State College J. Sci., 23, 381–395, 1949.
[246] Pearcy, C., A complete set of unitary invariants for 3×3 complex matrices, Trans. Am. Math. Soc., 104(3), 425–429, 1962.
[247] Peng, S. H. and W. V., Chang, A compressible approach in finite element analysis of rubber-elastic material, Comput. Struct., 62(3), 573–593, 1997.
[248] Penn, R.W., Volume changes accompanying the extension of rubber, Trans. Soc. Rheol., 14(4), 509–517, 1970.
[249] Pennisi, S. and M., Trovato, On the irreducibility of Professor G. F. Smithapos;s representations for isotropic functions, Int. J. Eng. Sci., 25(8), 1059–1065, 1987.
[250] Pericak-Spector, K. A. and S. J., Spector, On the representation theorem for linear, isotropic tensor functions, J. Elast., 39(2), 181–185, 1995.
[251] Pericak-Spector, K. A., J., Sivaloganathan and S. J., Spector, The representation theorem for linear, isotropic tensor functions in even dimensions, J. Elast., 57(2), 157–164, 1999.
[252] Peyraut, F., Z. Q., Feng, Q. C., He, N., Labed, Robust numerical analysis of homogeneous and non-homogeneous deformations, Appl. Num. Math., 59(7), 1499–1514, 2009.
[253] Piero, G. D., Some properties of the set of fourth-order tensors, with application to elasticity, J. Elast., 9(3), 245–261, 1979.
[254] Podio–Guidugli, P., The Piola–Kirchhoff stress may depend linearly on the deformation gradient, J. Elast., 17(2), 183–187, 1987.
[255] Polya, G., Torsional rigidity, principal frequency, electrostatic capacity and symmetrization, Quart. Appl. Math., 6(3), 267–277, 1948.
[256] Polya, G. and A., Weinstein, On the torsional rigidity of multiply connected crosssections, Ann. Math., 52(1), 154'163, 1950.
[257] Poschl, T., Bisherige losungen des torsionsproblems fur drehkorper, Z. Angew Math. Mech., 2/(2), 137–147, 1922.
[258] Power, L. D. and S. B., Childs, Axisymmetric stresses and displacements in a finite circular bar, Int. J. Eng. Sci., 9(2), 241–255, 1971.
[259] Putzer, E. J., Avoiding the Jordan canonical form in the discussion of linear systems with constant coefficients, Am. Math. Monthly, 73(1), 2–7, 1966
[260] Qi, L., Eigenvalues and invariants of tensors, J. Math. Anal. Appl., 325(2), 1363–1377, 2007.
[261] Ramachandra Rao, B. S., C. S., Kale and R. P., Shimpi, The sector problem in plane elastostatics, Int. J. Eng. Sci., 11(5), 531–542, 1973.
[262] Ramachandra Rao, B. S., A. K., Kandya and S., Gopalacharyulu, Axial eigenfunctions for the axisymmetric problem of an elastic circular cylinder, Int. J. Eng. Sci., 14(1), 99–112, 1976.
[263] Rayleigh, L., On waves propagated along the plane surface of an elastic solid, Proc. London Math. Soc., 17, 4–11, 1885.
[264] Reese, S. and P., Wriggers, Material instabilities of an incompressible elastic cube under triaxial tension, Int. J. Solids Struct., 34(26), 3433–3454, 1997.
[265] Reese, S., On material and geometrical instabilities in finite elasticity and elastoplasticity, Arch. Mech. 52(6), 969–999, 2000.
[266] Reese, S. and S., Govindjee, A theory of finite viscoelasticity and numerical aspects, Int. J. Solids Struct., 35(26–27), 3455–3482, 1998.
[267] Reissner, E., Note on the problem of St. Venant flexure, Z. Angew Math. Phys., 15(2), 198–200, 1964.
[268] Rivlin, R. S., Universal relations for elastic materials, Rendiconti di Matematica, Seri VII, Roma, 20, 35–55, 2000.
[269] Rivlin, R. S. and M. F., Beatty, Dead loading of a unit cube of compressible isotropic elastic material, Z. Angew Math. Phys., 54(6), 954–963, 2003.
[270] Robbins, C. I. and R. C. T., Smith, A table of roots of sin z = −z. Phil. Mag., 39 (299), 1004–1005, 1948.
[271] Robert, M. and L. M., Keer, An elastic circular cylinder with displacement prescribed at the ends–axially symmetric case, Quart. J. Mech. Appl. Math., 40(3), 339–363, 1987.
[272] Rosati, L., Derivatives and rates of the stretch and rotation tensors, J. Elast., 56(3),213–230, 1999.
[273] Rosati, L., A novel approach to the solution of the tensor equation AX + XA = H, Int. J. Solids Struct., 37(25), 3457–3477, 2000.
[274] Rostamian, R., The completeness of Maxwellaapos;s stress function representation, J. Elast., 9(4), 349–356, 1979.
[275] Saccomandi, G. and R. C., Batra, Additional universal relations for transversely isotropic elastic materials, Math. Mech. Solids, 9(2), 167–174, 2004.
[276] Sadosky, M. A. and E., Sternberg, Stress concentrations around a triaxial ellipsoidal cavity, ASME J. Appl. Mech., 16(2), 149–157, 1949.
[277] Sadowsky, M. A. and E., Sternberg, Pure bending of an incomplete torus, ASME J. Appl. Mech., 20(2), 215–226, 1953.
[278] Saito, H., The axially symmetrical deformation of a short circular cylinder, Trans. Jap. Soc. Mech. Engr., 18(68), 21–28, 1952.
[279] Saito, H., On the stress distribution in a rotating circular disk of constant thickness, Trans. Jap. Soc. Mech. Engr., 18(75), 40–43, 1952.
[280] Saravanan, U. and K. R., Rajagopal, Inflation, extension, torsion and shearing of an inhomogeneous compressible elastic right circular annular cylinder, Math. Mech. Solids, 10(6), 603–650, 2005.
[281] Saravanan, U. and K. R., Rajagopal, On some finite deformations of inhomogeneous elastic solids, Math. Proc. R. Irish Academy, 107A(1), 43–72, 2007.
[282] Scheidler, M., The tensor equation AX + XA = Ψ(A, H), with applications to kinematics of continua, J. Elast., 36(2), 117–153, 1994.
[283] Seegar, M. and K., Pearson, De Saint-Venant solution for the flexure of cantilevers of cross-Section in the form of complete and curtate circular sectors, and on the influence of the manner of fixing the built-in end of the cantilever on its deflection, Proc. R. Soc.London Ser. A, 96(676), 211–232, 1919.
[284] Seth, B. R., On flexure in prisms with cross-sections of uniaxial symmetry, Proc. London Math. Soc., s2–37(1), 502–511, 1934.
[285] Seth, B. R., On flexure of beams of triangular cross-section, Proc. London Math. Soc., s2–41(5), 323–331, 1936.
[286] Seth, B. R., On the flexure of a hollow shaft-I, Proc. Math. Sci., 4(5), 531–541, 1936.
[287] Shames, I. H. and C., Dym, Energy and Finite Element Methods in Structural Mechanics, New York: Hemisphere Publishing Co., 1985.
[288] Sheehan, J. P. and L., Debnath, Transient vibrations of an isotropic elastic sphere, Pure and Applied Geophysics, 99(1), 37–48, 1972.
[289] Shepherd, W. M., Torsion of a cracked shaft, Engineering, 128(3313), 39–39, 1929.
[290] Shepherd, W. M., The torsion and flexure of shafting with keyways or cracks, Proc. R. Soc. London Ser. A, 138(836), 607–634, 1932.
[291] Shepherd, W. M., The flexure of a prism with cross-section bounded by a cardioid, Proc. R. Soc. London Ser. A, 154(882), 500–509, 1936.
[292] Shield, R. T., Deformations possible in every compressible, isotropic, perfectly elastic material, J. Elast., 1(1), 91–92, 1971.
[293] Shnaid, I., Thermodynamically consistent description of heat conduction with finite speed of heat propagation, Int. J. Heat Mass Transfer, 46(20), 3583–3863, 2003.
[294] Sibirskii, K. S., A minimal polynomial basis of unitary invariants of a square matrix of the third order, Matematicheskie Zametki, 3(3), 291–296, 1968.
[295] Silhavy, M., The Mechanics and Thermodynamics of Continuous Media, Berlin: Springer- Verlag, 1997.
[296] Simo, J. C., Algorithms for static and dynamic multiplicative plasticity that preserve the classical return mapping schemes of the infinitesimal theory, Comput. Methods Appl. Mech. Eng., 99(1), 61–112, 1992.
[297] Singh, R. P. and C. S., Jog, A hybrid finite element formulation for flexible multibody dynamics, J. Multi-body Dynamics, Proc. Institution Mech. Eng. Part K, DOI:10.1177/1464419315569622.
[298] Smith, O. K., Eigenvalues of a symmetric 3 × 3 matrix, Comm. ACM, 4(4), 168–168, 1961.
[299] Snell, C., The twisted sphere, Mathematika, 4(02), 162–165, 1957.
[300] Sokolnikoff, I. S., Mathematical Theory of Elasticity, Florida: Robert E. Krieger Publishing Company, 1987.
[301] Sokolnikoff, I.S. and E.S., Sokolnikoff, Torsion of regions bounded by circular arcs, Bull. Am. Math. Soc., 44(3), 384–387, 1938.
[302] Southwell, R.V., Castigliano's principle of minimum strain-energy and the conditions of compatibility for strain, S. Timoshenko, 60th Anniversary Volume, 1938, 211–217.
[303] Sparrow, E.M., Laminar flow in isosceles triangular ducts, A.I.Ch.E. J., 8(5), 599–604, 1962.
[304] Srinivasan, T.P., Decomposition of tensors representing physical properties of crystals, J. Phys.: Condens. Matter, 10(16), 3849–3496, 1998.
[305] Stephenson, R.A., On the uniqueness of the square-root of a symmetric, positive definite tensor, J. Elast., 10(2), 213–214, 1980.
[306] Sternberg, E. and F., Rosenthal, The elastic sphere under concentrated loads, ASME J. Appl. Mech., 19, 413–421, 1952.
[307] Sternberg, E., Three-dimensional stress concentrations in the theory of elasticity, Appl. Mech. Rev., 11(1), 1–4, 1958.
[308] Sternberg, E., On the integration of the equations of motion in the classical theory of elasticity, Arch. Rational Mech. Anal., 6(1), 34–50, 1960.
[309] Stevenson, A.C., Flexure with shear and associated torsion in prisms of uni-axial and asymmetric cross-sections, Phil. Trans. R. Soc. London Ser. A., 237(776), 161–229, 1938.
[310] Stevenson, A.C., The torsion and flexure solutions for the elliptic limacon cross-section, Proc. London Math. Soc., s2ndash;45(1), 126–143, 1939.
[311] Stevenson, A.C., Complex potentials in two-dimensional elasticity, Proc. R. Soc. London Ser. A., 184(997), 129–179, 1945.
[312] Stevenson, A.C., The centre of flexure of a hollow shaft, Proc. London Math. Soc., s2ndash;50(1), 536–549, 1949.
[313] Stewart, I.W., The Static and Dynamic Continuum Theory of Liquid Crystals, London: Taylor and Franscis, 2004.
[314] Straughan, B., Heat waves, New York: Springer, 2011.
[315] Sussman, T. and K.J., Bathe, A finite element formulation for nonlinear incompressible elastic and inelastic analysis, Comput. Struct., 26 (1/2), 357–409, 1987.
[316] Svendsen, B. and A., Bertram, On frame-indifference and form-invariance in constitutive theory, Acta Mech., 132(1–4), 195–207, 1999.
[317] Swan, G.W., The semi-infinite cylinder with prescribed end-displacements, SIAM J. Appl. Math., 16(4), 860–881, 1968.
[318] Sylvester, J. and G., Uhlmann, A global uniqueness theorem for an inverse boundary value problem, Ann. Math., 125(1), 153–169, 1987.
[319] Tang, S., Elastic stresses in rotating anisotropic disks, Int. J. Mech. Sci., 11(6), 5097ndash;517, 1969.
[320] Tarantino, A.M., Homogeneous equilibrium configurations of a hyperelastic compressible cube under equitriaxial dead-load tractions, J. Elast., 92(3), 227–254, 2008.
[321] Tarn, J-Q., Stress singularity in an elastic cylinder of cylindrically anisotropic materials, J. Elast., 69(1–3), 1–13, 2002.
[322] Tarn, J-Q., Tseng, W-D. and Chang, H-H., A circular elastic cylinder under its own weight, Int. J. Solids Struct., 46(14), 2886–2896, 2009.
[323] Thompson, T.R. and R.W., Little, End effects in a truncated semi-infinite cone, Quart. J. Mech. Appl. Math., 23(2), 185–195, 1970.
[324] Timoshenko, S.P. and J.N., Goodier, Theory of Elasticity, New York: McGraw-Hill Book Company, 1970.
[325] Ting, T.C.T., The wedge subjected to tractions: a paradox re-examined, J. Elast., 14(3), 235–247, 1984.
[326] Ting, T.C.T., Determination of C1/2, C−1/2 and more general isotropic tensor functions of C, J. Elast., 15(3), 319–323, 1985.
[327] Ting, T.C.T., New expressions for the solution of the matrix equation ATX + XA = H, J. Elast., 45(1), 61–72, 1996.
[328] Ting, T.C.T., The remarkable nature of radially symmetric deformation of spherically uniform linear anisotropic elastic solids, J. Elast., 53(1), 47–64, 1999.
[329] Ting, T.C.T., New solutions to pressuring, shearing, torsion and extension of a cylindrically anisotropic elastic circular tube or bar, Proc. R. Soc. London Ser. A, 455(1989), 3527–3542, 1999.
[330] Tokovyy, Y.V., K.M., Hung and C.C., Ma, Determination of stresses and displacements in a thin annular disk subjected to diametral compression, J. Math. Sci., 165(3), 342–354, 2010.
[331] Tolf, G., Saint-Venant Bending of an Orthotropic Beam, Composite Struct., 4(1), 1–14, 1985.
[332] Tortorelli, D.A., A generalized formulation of elastodynamics: Small on rigid, J. Elast., 105(1–2), 349–363, 2011.
[333] Tranter, C. J., The application of the Laplace transformation to a problem on elastic vibrations, Phil. Mag., 33(223), 614–622, 1942.
[334] Truesdell, C.A First Course in Rational Continuum Mechanics, London: Academic Press, 1977.
[335] Truesdell, C.Rational Thermodynamics, New York: Springer-Verlag, 1984.
[336] Truesdell, C.An Idiot's Fugitive Essays on Science, New York: Springer-Verlag, 1984.
[337] Truesdell, C. and W., NollThe Non-linear Field Theories of Mechanics, Handbuch der Physik 3, Berlin: Springer-Verlag, 1965.
[338] Tsamasphyros, G. and P. S., Theocaris, On the solution of the sector problem, J. Elast., 9(3), 271–281, 1979.
[339] Tsuchida, E. and I., Nakahara, Three-dimensional stress concentration around a spherical cavity in a semi-infinite elastic body, Bull. Jap. Soc. Mech. Eng., 13(58), 499–508, 1970.
[340] Tsuchida, E. and T., Uchiyama, Stresses in an elastic circular cylinder with a prolate spheroidal cavity under tension, Bull. Jap. Soc. Mech. Eng., 22(166), 476–482, 1979.
[341] Tsuchida, E. andT., Uchiyama, Stresses in an elastic circular cylinder with an oblate spheroidal cavity or an internal penny-shaped crack under tension, Bull. Jap. Soc. Mech. Eng., 23(175), 1–8, 1980.
[342] Uchiyama, T. and E., Tsuchida, Stresses in an elastic circular cylinder with a prolate spheroidal cavity under torsion, J. Elast., 20(1), 41–52, 1988.
[343] Ulitko, A. F., Stress state of a hollow sphere loaded by concentrated forces, Prikladnaya Mekhanika, 4(5), 38–45, 1968.
[344] Vallee, C., Q., He and C., Lerintiu, Convex analysis of the eigenvalues of a 3D secondorder symmetric tensor, J. Elast., 83(2), 191–204, 2006.
[345] Vujosevic, L. and V. A., Lubarda, Finite-strain thermoelasticity based on multiplicative decomposition of deformation gradient, Theo. Appl. Mech., 28–29, 379–399, 2002.
[346] Wang, W. and M. Z., Wang, Constructivity and completeness of the general solutions in elastodynamics, Acta Mech., 91(3–4), 209–214, 1992.
[347] Wang, X. and Y., Gong, A theoretical solution for axially symmetric problems in elastodynamics, Acta Mech. Sinica, 7(3), 275–282, 1991.
[348] Washizu, K., A note on the conditions of compatibility, J. Math. Phys., 36(4), 306–312, 1958.
[349] Watson, G. N., A Treatise on the Theory of Bessel Functions, London: Cambridge University Press, Second Edition, 1966.
[350] Wermuth, E. M. E., Two remarks on matrix exponentials, Lin. Alg. Appl., 117, 127–132, 1989.
[351] Wheeler, L. T. and E., Sternberg, Some theorems in classical elastodynamics, Arch. Rational Mech. Anal., 31(1), 51–90, 1968.
[352] Wheeler, L. T., On the derivatives of the stretch and rotation with respect to the deformation gradient, J. Elast., 24(1–3), 129–133, 1990.
[353] Wolfram, S., Mathematica, Champaign, Illinois: Wolfram Research Inc., 2014.
[354] Wood, J. A., The chain rule for matrix exponential functions, College Math. J., 35(3), 220–222, 2004.
[355] Xiao, H., Unified explicit basis-free expressions for time rate and conjugate stress of an arbitrary Hill's strain, Int. J. Solids Struct., 32(22), 3327–3340, 1995.
[356] Xiao, H., O. T., Bruhns, and A., Meyers, On objective corotational rates and their defining spin tensors, Int. J. Solids Struct., 35(30), 4001–4014, 1998.
[357] Xiao, H., O. T., Bruhns, and A., Meyers, Existence and uniqueness of the integrable-exactly hypoelastic equation its significance to finite inelasticity, Acta Mech., 138(1), 31–50, 1999.
[358] Yavari, A., Compatibility equations of nonlinear elasticity for non-simply connected bodies, Arch. Rational Mech. Anal., 209(1), 237–253, 2013.
[359] Young, A. W., E. M., Elderton, K., Pearson, On the torsion resulting from flexure in prisms with cross-sections of uniaxial symmetry only, Draper' Company Memoirs, Technical Ser. VII, 1918.
[360] Zheng, X. and P., Palffy-Muhoray, Eigenvalue decomposition for tensors of arbitrary rank, Electronic-Liquid Crystal Communication, 2007.
[361] Zidi, M., Combined torsion, circular and axial shearing of a compressible hyperelastic and prestressed tube, ASME J. Appl. Mech., 67(1), 33–40, 2000.