Journal of Pure and Applied Mathematics: Advances and Applications[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.
