References

A NON-CLASSICAL INTERNAL PLOAR CONTINUUM THEORY FOR FINITE DEFORMATION OF SOLIDS USING FIRST PIOLA-KIRCHHOFF STRESS TENSOR


[1] K. S. Surana, M. J. Powell, and J. N. Reddy. A more complete thermodynamic framework for solid continua. Journal of Thermal Engineering, 1(1):1–13, 2015.

[2] K. S. Surana, J. N. Reddy, D. Nunez, and M. J. Powell. A polar continuum theory for solid continua. International Journal of Engineering Research and Industrial Applications, 8(2):77–106, 2015.

[3] A. C. Eringen. Mechanics of Micromorphic Materials. H. Gortler (ed.) Proc. 11th Intern. Congress. Appl. Mech., pages 131–138, 1964a.

[4] A. C. Eringen. Mechanics of Micromorphic Continua. E. Kroner(ed.) Mechanics of Generalized Continua, pages 18–35, 1968.

[5] A. C. Eringen. Theory of micropolar elasticity. H. Liebowitz (ed.) Fracture, pages 621–729, 1968.

[6] A. C. Eringen. Balance Laws of Micromorphic Mechanics. International Journal of Engineering Science, 8(10):819–828, 1970.

[7] A. C. Eringen. Theory of Thermo-Microstretch Fluids and Bubbly Liquids. International Journal of Engineering Science, 28(2):133–143, 1990.

[8] A. C. Eringen. Theory of Micropolar Elasticity. Springer, 1990.

[9] A. C. Eringen. A Unified Theory of Thermomechanical Materials. International Journal of Engineering Science, 4:179–202, 1966.

[10] A. C. Eringen. Linear Theory of Micropolar Viscoelasticity. International Journal of Engineering Science, 5:191–204, 1967.

[11] A. C. Eringen. Theory of Micromorphic Materials with Memory. International Journal of Engineering Science, 10:623–641, 1972.

[12] W. Koiter. Couple Stresses in the Theory of Elasticity, i and ii. Nederl. Akad. Wetensch. Proc. Ser. B, 67:17–44, 1964.

[13] W. Oevel and J. Schröter. Balance Equations for Micromorphic Materials. Journal of Statistical Physics, 25(4):645–662, 1981.

[14] J. N. Reddy. Nonlocal Theories for Bending, Buckling and Vibration of Beams. International Journal of Engineering Science, 45:288–307, 2007.

[15] J. N. Reddy and S. D. Pang. Nonlocal Continuum Theories of Beams for the Analysis of Carbon Nanotubes. Journal of Applied Physics, 103, 023511, 2008.

[16] J. N. Reddy. Nonlocal nonlinear Formulations for Bending of Classical and Shear Deformation Theories of Beams and Plates. International Journal of Engineering Science, 48:1507–1518, 2010.

[17] P. Lu, P. Q. Zhang, H. P. Leo, C. M. Wang, and J. N. Reddy. Nonlocal Elastic Plate Theories. Proceedings of Royal Society A, 463:3225–3240, 2007.

[18] J. F. C. Yang and R. S. Lakes. Experimental Study of Micropolar and Couple Stress Elasticity in Compact Bone in Bending. Journal of Biomechanics, 15(2):91–98, 1982.

[19] V. A. Lubarda and X. Markenscoff. Conservation Integrals in Couple Stress Elasticity. Journal of Mechanics and Physics of Solids, 48:553–564, 2000.

[20] H. M. Ma, X. L. Gao, and J. N. Reddy. A Microstructure-dependent Timoshenko Beam Model Based on a Modified Couple Stress Theory. Journal of Mechanics and Physics of Solids, 56:3379–3391, 2008.

[21] H. M. Ma, X. L. Gao, and J. N. Reddy. A Nonclassical Reddy-Levinson Beam Model Based on Modified Couple Stress Theory. Journal of Multiscale Computational Engineering, 8(2):167–180, 2010.

[22] J. N. Reddy. Microstructure Dependent Couple Stress Theories of Functionally Graded Beams. Journal of Mechanics and Physics of Solids, 59:2382–2399, 2011.

[23] J. N. Reddy and A. Arbind. Bending Relationship Between the Modified Couple Stress-based Functionally Graded Timoshenko Beams and Homogeneous Bernoulli-Euler Beams. Ann. Solid Struc. Mech., 3:15–26, 2012.

[24] A. R. Srinivasa and J. N. Reddy. A Model for a Constrained, Finitely Deforming Elastic Solid with Rotation Gradient Dependent Strain Energy and its Specialization to Von Kármán Plates and Beams. Journal of Mechanics and Physics of Solids, 61(3):873–885, 2013.

[25] R. J. Mora and A. M. Waas. Evaluation of the Micropolar Elasticity Constants for Honeycombs. Acta Mechanica, 192:1–16, 2007.

[26] P. R. Onck. Cosserat Modeling of Cellular Solids. C. R. Mecanique, 330:717–722, 2002.

[27] P. H. Segerstad, S. Toll, and R. Larsson. A Micropolar Theory for the Finite Elasticity of Open-cell Cellular Solids. Proceedings of Royal Society A, 465:843–865, 2009.

[28] H. Altenbach and V. A. Eremeyev. On the linear theory of micropolar plates. ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 89(4):242–256, 2009.

[29] H. Altenbach and V. A. Eremeyev. Strain rate tensors and constitutive equations of inelastic micropolar materials. International Journal of Plasticity, 63:3–17, 2014.

[30] H. Altenbach, V. A. Eremeyev, L. P. Lebedev, and L. A. Rendón. Acceleration waves and ellipticity in thermoelastic micropolar media. Archive of Applied Mechanics, 80(3):217–227, 2010.

[31] H. Altenbach, G. A. Maugin, and V. Erofeev. Mechanics of generalized continua, volume 7. Springer, 2011.

[32] H. Altenbach, K. Naumenko, and P. A. Zhilin. A micro-polar theory for binary media with application to phase-transitional flow of fiber suspensions. Continuum Mechanics and Thermodynamics, 15(6):539–570, 2003.

[33] F. Ebert. A similarity solution for the boundary layer flow of a polar fluid. The Chemical Engineering Journal, 5(1):85–92, 1973.

[34] V. A. Eremeyev, L. P. Lebedev, and H. Altenbach. Kinematics of micropolar continuum. In Foundations of Micropolar Mechanics, pages 11–13. Springer, 2013.

[35] V. A. Eremeyev and W. Pietraszkiewicz. Material symmetry group and constitutive equations of anisotropic Cosserat continuum. Generalized Continua As Models for Materials, page 10, 2012.

[36] V. A. Eremeyev and W. Pietraszkiewicz. Material symmetry group of the non-linear polar-elastic continuum. International Journal of Solids and Structures, 49(14):1993–2005, 2012.

[37] E. F. Grekova. Ferromagnets and Kelvin’s medium: Basic equations and wave processes. Journal of Computational Acoustics, 9(02):427–446, 2001.

[38] E. F. Grekova. Linear reduced Cosserat medium with spherical tensor of inertia, where rotations are not observed in experiment. Mechanics of Solids, 47(5):538–543, 2012.

[39] E. F. Grekova, M. A. Kulesh, and G. C. Herman. Waves in linear elastic media with microrotations, part 2: Isotropic reduced Cosserat model. Bulletin of the Seismological Society of America, 99(2B):1423–1428, 2009.

[40] G. Grioli. Linear micropolar media with constrained rotations. In Micropolar Elasticity, pages 45–71. Springer, 1974.

[41] E. F. Grekova and G. A. Maugin. Modelling of complex elastic crystals by means of multi-spin micromorphic media. International Journal of Engineering Science, 43(5):494–519, 2005.

[42] G. Grioli. Microstructures as a refinement of cauchy theory. problems of physical concreteness. Continuum Mechanics and Thermodynamics, 15(5):441–450, 2003.

[43] J. Altenbach, H. Altenbach, and V. A. Eremeyev. On generalized Cosserat-type theories of plates and shells: a short review and bibliography. Archive of Applied Mechanics, 80(1):73–92, 2010.

[44] M. Lazar and G. A. Maugin. Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity. International Journal of Engineering Science, 43(13):1157–1184, 2005.

[45] M. Lazar and G.A. Maugin. Defects in gradient micropolar elasticity âĂŤI: screw dislocation. Journal of the Mechanics and Physics of Solids, 52(10):2263–2284, 2004.

[46] G. A. Maugin. A phenomenological theory of ferroliquids. International Journal of Engineering Science, 16(12):1029–1044, 1978.

[47] G. A. Maugin. Wave motion in magnetizable deformable solids. International Journal of Engineering Science, 19(3):321–388, 1981.

[48] G. A. Maugin. On the structure of the theory of polar elasticity. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 356(1741):1367–1395, 1998.

[49] W. Pietraszkiewicz and V. A. Eremeyev. On natural strain measures of the non-linear micropolar continuum. International Journal of Solids and Structures, 46(3):774–787, 2009.

[50] E. Cosserat and F. Cosserat. Théorie des corps déformables. Paris, 1909.

[51] A. V. Zakharov and E. L. Aero. Statistical mechanical theory of polar fluids for all densities. Physica A: Statistical Mechanics and its Applications, 160(2):157–165, 1989.

[52] A. E. Green. Micro-materials and multipolar continuum mechanics. International Journal of Engineering Science, 3(5):533–537, 1965.

[53] A. E. Green and R. S. Rivlin. The relation between director and multipolar theories in continuum mechanics. Zeitschrift für angewandte Mathematik und Physik ZAMP, 18(2):208–218, 1967.

[54] A. E. Green and R. S. Rivlin. Multipolar continuum mechanics. Archive for Rational Mechanics and Analysis, 17(2):113–147, 1964.

[55] L. C. Martins, R. F. Oliveira, and P. Podio-Guidugli. On the vanishing of the additive measures of strain and rotation for finite deformations. Journal of elasticity, 17(2):189–193, 1987.

[56] L. C. Martins and P. Podio-Guidugli. On the local measures of mean rotation in continuum mechanics. Journal of elasticity, 27(3):267–279, 1992.

[57] W. Nowacki. Theory of micropolar elasticity. Springer, 1970.

[58] F. A. C. M. Yang, A. C. M. Chong, D. C. C. Lam, and P. Tong. Couple stress based strain gradient theory for elasticity. International Journal of Solids and Structures, 39(10):2731–2743, 2002.

[59] A. C. Eringen. Mechanics of continua. Huntington, NY, Robert E. Krieger Publishing Co., 1980. 606 p., 1, 1980.

[60] J. N. Reddy. An introduction to continuum mechanics. Cambridge University Press, Cambridge, 2013.

[61] K. S. Surana. Advanced Mechanics of Continua. CRC/Taylor and Francis, Boca Raton, FL, 2015.

[62] K. S. Surana, Y. Ma, A. Romkes, and J. N. Reddy. The rate constitutive equations and their validity for progressively increasing deformation. Mechanics of Advanced Materials and Structures, 17(7):509–533, 2010.

[63] P. Steinmann. A micropolar theory of finite deformation and finite rotation multiplicative elastoplasticity. International Journal of Solids and Structures, 31(8):1063–1084, 1994.

[64] A. R. Srinivasa and J. N. Reddy. A model for a constrained, finitely deforming, elastic solid with rotation gradient dependent strain energy, and its specialization to von Kármán plates and beams. Journal of Mechanics and Physics of Solids, 61(3):873–885, 2013.

[65] P. H. Segerstad, S. Toll, and R. Larsson. A micropolar theory for the finite elasticity of open-cell cellular solids. Proceedings of the Royal Society A, 465:843–865, 2008.

[66] R. T. Shield. The rotation associated with large strains. SIAM Journal on Applied MAthematics, 25(3):483–491, 1973.