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1. | Department of Mathematics, "Al.I. Cuza" University, and Octav Mayer Institute of Mathematics (Romanian Academy), 700508, Iaşi, Romania |
References:
[1] |
E. C. Aifantis, Exploring the applicability of gradient elasticity to certain micro/ nano reliability problems, Microsystem Technology, 15 (2009), 109-115.
doi: 10.1007/s00542-008-0699-8. |
[2] |
G. Amendola, M. Fabrizio and J. M. Golden, Thermodynamics of a non-simple heat conductor with memory, Quart. Appl. Math., 69 (2011), 787-806.
doi: 10.1090/S0033-569X-2011-01228-5. |
[3] |
G. Amendola, M. Fabrizio and J. M. Golden, Second gradient viscoelastic fluids: Dissipation principle and free energies, Meccanica, 47 (2012), 1859-1868.
doi: 10.1007/s11012-012-9559-9. |
[4] |
H. Askes and E. C. Aifantis, Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results, Int. J. Solids Struct., 48 (2011), 1962-1990.
doi: 10.1016/j.ijsolstr.2011.03.006. |
[5] |
O. Brulin and S. Hjalmars, Linear grade consistent micropolar theory, Int. J. Eng. Sci., 19 (1981), 1731-1738.
doi: 10.1016/0020-7225(81)90163-4. |
[6] |
L. Brun, Methodes energetiques dans les systemes evolutifs lineaires, J. Mecanique, 8 (1969), 125-166. |
[7] |
D. E. Carlson, Linear Thermoelasticity, in Handbuch der Physik, vol. VIa/2, (ed. C. Truesdell), Springer-Verlag, Berlin-Heidelberg-New York, 1972. |
[8] |
S. Chirita, Uniqueness and continuous dependence results for the incremental thermoelasticity, J. Thermal Stresses, 5 (1982), 331-346.
doi: 10.1080/01495738208942154. |
[9] |
O. Coussy, Mechanics and Physics of Porous Solids, John Wiley and Sons, Chichester, 2010.
doi: 10.1002/9780470710388. |
[10] |
S. C. Cowin and J. W. Nunziato, Linear elastic materials with voids, J. Elasticity, 13 (1983), 125-147.
doi: 10.1007/BF00041230. |
[11] |
T. Dillard, S.Forest and P. Ienny, Micromorphic continuum modelling of the deformation and fracture behaviour of nickel foams, Eur.J. Mech.-A/Solids, 25 (2006), 526-549.
doi: 10.1016/j.euromechsol.2005.11.006. |
[12] |
A. C. Eringen and E. S. Suhubi, Nonlinear theory of simple microelastic solids, Int. J. Eng. Sci., 2 (1964), 189-203.
doi: 10.1016/0020-7225(64)90004-7. |
[13] |
A. C. Eringen, Microcontinuum Field Theories. I: Foundations and Solid, Springer- Verlag, New York, Berlin, Heidelberg, 1999.
doi: 10.1007/978-1-4612-0555-5. |
[14] |
M. Fabrizio and A. Morro, Mathematical Problems in Linear Viscoelasticity, SIAM Studies in Applied Mathematics 12, Philadelphia, PA, USA, 1992.
doi: 10.1137/1.9781611970807. |
[15] |
S. Forest, J. M. Cardona and R. Sievert, Thermoelasticity of second- grade media, in Continuum Thermomechanics, The Art and Science of Modelling Material Behaviour, Paul Germain's Anniversary Volume, (eds. G.A. Maugin, R. Drouot and F. Sidoroff.), Kluwer Academic Publishers, (2000), 163-176. |
[16] |
P. Giovine, Linear wave motions in continua with nano-pores, in Wave Processes in Classical and New Solids, (ed. P. Giovine), Publisher: InTech, (2012), 62-86. |
[17] |
A. E. Green, Thermoelastic stresses in initially stressed bodies, Proc. Roy. Soc. London, Ser. A, 266 (1962), 1-19.
doi: 10.1098/rspa.1962.0043. |
[18] |
A. E. Green and R. S. Rivlin, Multipolar continuum mechanics, Arch. Rational Mech.Anal., 17 (1964), 113-147. |
[19] |
S. Hjalmars, Non-linear micropolar theory, in Mechanics of Micropolar Media, (eds. O. Brulin and R.K.T. Hsieh), World Scientific, Singapore, (1982), 147-189, |
[20] |
D. Iesan, Incremental equations in thermoelasticity, J. Thermal Stresses, 3 (1980), 41-56. |
[21] |
D. Iesan, Prestressed Bodies, Pitman Research Notes in Mathematics Series 195, Longman Scientific and Technical, Longman House, Harlow, Essex, UK and John Wiley & Sons, Inc., New York, 1989. |
[22] |
D. Iesan, Thermoelastic Models of Continua, Kluwer Academic, Dordrecht, 2004.
doi: 10.1007/978-1-4020-2310-1. |
[23] |
R. J. Knops and E. W. Wilkes, Theory of elastic stability, in Handbuch der Physik, (ed. C. Truesdell), Springer-Verlag, Berlin Heidelberg-New York, 1973. |
[24] |
R. J. Knops and L. E. Payne, Uniqueness Theorems in Linear Elasticity, Springer Tracts in Natural Philosophy, vol. 19, Berlin-Heidelberg-New York, 1971. |
[25] |
R. J. Knops, Uniqueness and continuous data dependence in the elastic cylinders, Int. J. Non-Linear Mech., 36 (2001), 489-499.
doi: 10.1016/S0020-7462(00)00078-0. |
[26] |
F. Martinez, F. and R. Quintanilla, On the incremental problem in thermoelasticity of nonsimple materials, Zeit. Angew.Math. Mech., 78 (1998), 703-710. |
[27] |
R. D. Mindlin, Microstructure in linear elasticity, Arch.Rational Mech.Anal., 16 (1964), 51-78. |
[28] |
R. D. Mindlin and N. N. Eshel, On first strain gradient theories in linear elasticity, Int. J. Solids Struct., 4 (1968), 109-124.
doi: 10.1016/0020-7683(68)90036-X. |
[29] |
C. B. Navarro and R. Quintanilla, On existence and uniqueness in incremental thermoelasticity, Zeit. Angew. Math. Mech., 35 (1984), 206-215.
doi: 10.1007/BF00947933. |
[30] |
P. Neff and S. Forest, A geometrically exact micromorphic model for elastic metallic foams accounting for affine microstructure. Modelling existence and minimizers, identification of moduli and computational results, J. Elasticity, 87 (2007), 239-276.
doi: 10.1007/s10659-007-9106-4. |
[31] |
W. Nowacki, Theory of Asymmetric Elasticity, Polish Scientific Publishers, Warszawa and Pergamon Press, Oxford, New York, Paris, Frankfurt, 1986. |
[32] |
J. W. Nunziato and S. C. Cowin, A nonlinear theory of elastic materials with voids,, Arch.Rational Mech.Anal., 72 (): 175.
doi: 10.1007/BF00249363. |
[33] |
A. Ochsner, G. E. Murch and M. J. S. Lemos, Cellular and Porous Materials, Wiley-VCH, Weinheim, 2008. |
[34] |
S. A. Papanicolopulos, Chirality in isotropic linear gradient elasticity, Int. J. Solids Struct., 48 (2011), 745-752.
doi: 10.1016/j.ijsolstr.2010.11.007. |
[35] |
C. Rymarz, On the model of non-simple medium with rotational degrees of freedom, Bull. Acad. Polon. Sci.,S. Sci. Techn., 16 (1968), 271-277. |
[36] |
G. Sciarra, F. Dell'Isola and O. Coussy, Second gradient poromechanics, Int. J. Solids Struct., 44 (2007), 6607-6629.
doi: 10.1016/j.ijsolstr.2007.03.003. |
[37] |
R. A. Toupin, Elastic materials with couple stresses, Arch.Rational Mech.Anal., 11 (1962), 385-414.
doi: 10.1007/BF00253945. |
[38] |
R. A. Toupin, Theories of elasticity with couple-stress, Arch. Rational Mech.Anal., 17 (1964), 85-112. |
[39] |
J. R. Vinson and R. L. Sierakowski, The Behaviour of Structures Composed of Composite Materials, Second edition, Kluwer Acad. Publ., Dordrecht, 2002. |
show all references
References:
[1] |
E. C. Aifantis, Exploring the applicability of gradient elasticity to certain micro/ nano reliability problems, Microsystem Technology, 15 (2009), 109-115.
doi: 10.1007/s00542-008-0699-8. |
[2] |
G. Amendola, M. Fabrizio and J. M. Golden, Thermodynamics of a non-simple heat conductor with memory, Quart. Appl. Math., 69 (2011), 787-806.
doi: 10.1090/S0033-569X-2011-01228-5. |
[3] |
G. Amendola, M. Fabrizio and J. M. Golden, Second gradient viscoelastic fluids: Dissipation principle and free energies, Meccanica, 47 (2012), 1859-1868.
doi: 10.1007/s11012-012-9559-9. |
[4] |
H. Askes and E. C. Aifantis, Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results, Int. J. Solids Struct., 48 (2011), 1962-1990.
doi: 10.1016/j.ijsolstr.2011.03.006. |
[5] |
O. Brulin and S. Hjalmars, Linear grade consistent micropolar theory, Int. J. Eng. Sci., 19 (1981), 1731-1738.
doi: 10.1016/0020-7225(81)90163-4. |
[6] |
L. Brun, Methodes energetiques dans les systemes evolutifs lineaires, J. Mecanique, 8 (1969), 125-166. |
[7] |
D. E. Carlson, Linear Thermoelasticity, in Handbuch der Physik, vol. VIa/2, (ed. C. Truesdell), Springer-Verlag, Berlin-Heidelberg-New York, 1972. |
[8] |
S. Chirita, Uniqueness and continuous dependence results for the incremental thermoelasticity, J. Thermal Stresses, 5 (1982), 331-346.
doi: 10.1080/01495738208942154. |
[9] |
O. Coussy, Mechanics and Physics of Porous Solids, John Wiley and Sons, Chichester, 2010.
doi: 10.1002/9780470710388. |
[10] |
S. C. Cowin and J. W. Nunziato, Linear elastic materials with voids, J. Elasticity, 13 (1983), 125-147.
doi: 10.1007/BF00041230. |
[11] |
T. Dillard, S.Forest and P. Ienny, Micromorphic continuum modelling of the deformation and fracture behaviour of nickel foams, Eur.J. Mech.-A/Solids, 25 (2006), 526-549.
doi: 10.1016/j.euromechsol.2005.11.006. |
[12] |
A. C. Eringen and E. S. Suhubi, Nonlinear theory of simple microelastic solids, Int. J. Eng. Sci., 2 (1964), 189-203.
doi: 10.1016/0020-7225(64)90004-7. |
[13] |
A. C. Eringen, Microcontinuum Field Theories. I: Foundations and Solid, Springer- Verlag, New York, Berlin, Heidelberg, 1999.
doi: 10.1007/978-1-4612-0555-5. |
[14] |
M. Fabrizio and A. Morro, Mathematical Problems in Linear Viscoelasticity, SIAM Studies in Applied Mathematics 12, Philadelphia, PA, USA, 1992.
doi: 10.1137/1.9781611970807. |
[15] |
S. Forest, J. M. Cardona and R. Sievert, Thermoelasticity of second- grade media, in Continuum Thermomechanics, The Art and Science of Modelling Material Behaviour, Paul Germain's Anniversary Volume, (eds. G.A. Maugin, R. Drouot and F. Sidoroff.), Kluwer Academic Publishers, (2000), 163-176. |
[16] |
P. Giovine, Linear wave motions in continua with nano-pores, in Wave Processes in Classical and New Solids, (ed. P. Giovine), Publisher: InTech, (2012), 62-86. |
[17] |
A. E. Green, Thermoelastic stresses in initially stressed bodies, Proc. Roy. Soc. London, Ser. A, 266 (1962), 1-19.
doi: 10.1098/rspa.1962.0043. |
[18] |
A. E. Green and R. S. Rivlin, Multipolar continuum mechanics, Arch. Rational Mech.Anal., 17 (1964), 113-147. |
[19] |
S. Hjalmars, Non-linear micropolar theory, in Mechanics of Micropolar Media, (eds. O. Brulin and R.K.T. Hsieh), World Scientific, Singapore, (1982), 147-189, |
[20] |
D. Iesan, Incremental equations in thermoelasticity, J. Thermal Stresses, 3 (1980), 41-56. |
[21] |
D. Iesan, Prestressed Bodies, Pitman Research Notes in Mathematics Series 195, Longman Scientific and Technical, Longman House, Harlow, Essex, UK and John Wiley & Sons, Inc., New York, 1989. |
[22] |
D. Iesan, Thermoelastic Models of Continua, Kluwer Academic, Dordrecht, 2004.
doi: 10.1007/978-1-4020-2310-1. |
[23] |
R. J. Knops and E. W. Wilkes, Theory of elastic stability, in Handbuch der Physik, (ed. C. Truesdell), Springer-Verlag, Berlin Heidelberg-New York, 1973. |
[24] |
R. J. Knops and L. E. Payne, Uniqueness Theorems in Linear Elasticity, Springer Tracts in Natural Philosophy, vol. 19, Berlin-Heidelberg-New York, 1971. |
[25] |
R. J. Knops, Uniqueness and continuous data dependence in the elastic cylinders, Int. J. Non-Linear Mech., 36 (2001), 489-499.
doi: 10.1016/S0020-7462(00)00078-0. |
[26] |
F. Martinez, F. and R. Quintanilla, On the incremental problem in thermoelasticity of nonsimple materials, Zeit. Angew.Math. Mech., 78 (1998), 703-710. |
[27] |
R. D. Mindlin, Microstructure in linear elasticity, Arch.Rational Mech.Anal., 16 (1964), 51-78. |
[28] |
R. D. Mindlin and N. N. Eshel, On first strain gradient theories in linear elasticity, Int. J. Solids Struct., 4 (1968), 109-124.
doi: 10.1016/0020-7683(68)90036-X. |
[29] |
C. B. Navarro and R. Quintanilla, On existence and uniqueness in incremental thermoelasticity, Zeit. Angew. Math. Mech., 35 (1984), 206-215.
doi: 10.1007/BF00947933. |
[30] |
P. Neff and S. Forest, A geometrically exact micromorphic model for elastic metallic foams accounting for affine microstructure. Modelling existence and minimizers, identification of moduli and computational results, J. Elasticity, 87 (2007), 239-276.
doi: 10.1007/s10659-007-9106-4. |
[31] |
W. Nowacki, Theory of Asymmetric Elasticity, Polish Scientific Publishers, Warszawa and Pergamon Press, Oxford, New York, Paris, Frankfurt, 1986. |
[32] |
J. W. Nunziato and S. C. Cowin, A nonlinear theory of elastic materials with voids,, Arch.Rational Mech.Anal., 72 (): 175.
doi: 10.1007/BF00249363. |
[33] |
A. Ochsner, G. E. Murch and M. J. S. Lemos, Cellular and Porous Materials, Wiley-VCH, Weinheim, 2008. |
[34] |
S. A. Papanicolopulos, Chirality in isotropic linear gradient elasticity, Int. J. Solids Struct., 48 (2011), 745-752.
doi: 10.1016/j.ijsolstr.2010.11.007. |
[35] |
C. Rymarz, On the model of non-simple medium with rotational degrees of freedom, Bull. Acad. Polon. Sci.,S. Sci. Techn., 16 (1968), 271-277. |
[36] |
G. Sciarra, F. Dell'Isola and O. Coussy, Second gradient poromechanics, Int. J. Solids Struct., 44 (2007), 6607-6629.
doi: 10.1016/j.ijsolstr.2007.03.003. |
[37] |
R. A. Toupin, Elastic materials with couple stresses, Arch.Rational Mech.Anal., 11 (1962), 385-414.
doi: 10.1007/BF00253945. |
[38] |
R. A. Toupin, Theories of elasticity with couple-stress, Arch. Rational Mech.Anal., 17 (1964), 85-112. |
[39] |
J. R. Vinson and R. L. Sierakowski, The Behaviour of Structures Composed of Composite Materials, Second edition, Kluwer Acad. Publ., Dordrecht, 2002. |
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