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  • Cited by 7
  • Volume 1, 3rd edition
  • C. S. Jog, Indian Institute of Science, Bangalore
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Book description

Continuum mechanics studies the foundations of deformable body mechanics from a mathematical perspective. It also acts as a base upon which other applied areas such as solid mechanics and fluid mechanics are developed. This book discusses some important topics, which have come into prominence in the latter half of the twentieth century, such as material symmetry, frame-indifference and thermomechanics. The study begins with the necessary mathematical background in the form of an introduction to tensor analysis followed by a discussion on kinematics, which deals with purely geometrical notions such as strain and rate of deformation. Moving on to derivation of the governing equations, the book also presents applications in the areas of linear and nonlinear elasticity. In addition, the volume also provides a mathematical explanation to the axioms and laws of deformable body mechanics, and its various applications in the field of solid mechanics.

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Contents

References
[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.