-
Previous Article
Mathematical study of the small oscillations of a floating body in a bounded tank containing an incompressible viscous liquid
- DCDS-B Home
- This Issue
-
Next Article
Thermomechanics of hydrogen storage in metallic hydrides: Modeling and analysis
On the theory of viscoelasticity for materials with double porosity
1. | Institute for Fundamental and Interdisciplinary Mathematics Research, Ilia State University, K. Cholokashvili Ave., 3/5, 0162, Tbilisi, Georgia |
References:
[1] |
G. Amendola, M. Fabrizio and J. M. Golden, Thermodynamics of Materials with Memory: Theory and Applications, Springer, New York, Dordrecht, Heidelberg, London, 2012.
doi: 10.1007/978-1-4614-1692-0. |
[2] |
J. A. D. Appleby, M. Fabrizio, B. Lazzari and D. W. Reynolds, On exponential asymptotic stability in linear viscoelasticity, Mathematical Models and Methods in Applied Sciences, 16 (2006), 1677-1694.
doi: 10.1142/S0218202506001674. |
[3] |
G. I. Barenblatt, I. P. Zheltov and I. N. Kochina, Basic concept in the theory of seepage of homogeneous liquids in fissured rocks (strata), Journal of Applied Mathematics and Mechanics, 24 (1960), 1286-1303.
doi: 10.1016/0021-8928(60)90107-6. |
[4] |
J. G. Berryman and H. F. Wang, The elastic coefficients of double-porosity models for fluid transport in jointed rock, Journal of Geophysical Research, 100 (1995), 24611-24627.
doi: 10.1029/95JB02161. |
[5] |
J. G. Berryman and H. F. Wang, Elastic wave propagation and attenuation in a double-porosity dual-permiability medium, International Journal of Rock Mechanics and Mining Sciences, 37 (2000), 63-78.
doi: 10.1016/S1365-1609(99)00092-1. |
[6] |
D. E. Beskos and E. C. Aifantis, On the theory of consolidation with double porosity - II, International Journal of Engineering Science, 24 (1986), 1697-1716.
doi: 10.1016/0020-7225(86)90076-5. |
[7] |
M. A. Biot, General theory of three-dimensional consolidation, Journal of Applied Physics, 12 (1941), 155-164.
doi: 10.1063/1.1712886. |
[8] |
M. A. Biot, Theory of propagation of elastic waves in a fluid-saturated porous solid, I. Low frequency range, II. Higher frequency range, Journal of the Acoustical Society of America, 28 (1956), 179-191.
doi: 10.1121/1.1908241. |
[9] |
M. A. Biot, Mechanics of deformation and acoustic propagation in porous media, Journal of Applied Physics, 33 (1962), 1482-1498.
doi: 10.1063/1.1728759. |
[10] |
M. A. Biot, Theory of finite deformations of porous solids, Indiana University Mathematics Journal, 21 (1972), 597-620. |
[11] |
S. Chiriţă, C. Galeş and I. D. Ghiba, On spatial behavior of the harmonic vibrations in Kelvin-Voigt materials, Journal of Elasticity, 93 (2008), 81-92.
doi: 10.1007/s10659-008-9167-z. |
[12] |
R. M. Christensen, Theory of Viscoelasticity, 2nd ed., Dover Publ. Inc., Mineola, New York, 2010. |
[13] |
M. Ciarletta, F. Passarella and M. Svanadze, Plane waves and uniqueness theorems in the coupled linear theory of elasticity for solids with double porosity, Journal of Elasticity, 114 (2014), 55-68.
doi: 10.1007/s10659-012-9426-x. |
[14] |
M. Ciarletta and A. Scalia, On some theorems in the linear theory of viscoelastic materials with voids, Journal of Elasticity, 25 (1991), 149-158.
doi: 10.1007/BF00042463. |
[15] |
S. C. Cowin, The viscoelastic behavior of linear elastic materials with voids, Journal of Elasticity, 15 (1985), 185-191.
doi: 10.1007/BF00041992. |
[16] |
S. C. Cowin, Bone poroelasticity, Journal of Biomechanics, 32 (1999), 217-238.
doi: 10.1016/S0021-9290(98)00161-4. |
[17] |
S. C. Cowin, G. Gailani and M. Benalla, Hierarchical poroelasticity: Movement of interstitial fluid between levels in bones, Philosophical Transactions of the Royal Society A: mathematical, physical and engineering sciences, 367 (2009), 3401-3444.
doi: 10.1098/rsta.2009.0099. |
[18] |
S. De Cicco and L. Nappa, Singular surfaces in thermoviscoelastic materials with voids, Journal of Elasticity, 73 (2003), 191-210.
doi: 10.1023/B:ELAS.0000029961.09749.2b. |
[19] |
S. De Cicco and M. Svanadze, Fundamental solution in the theory of viscoelastic mixtures, Journal of Mechanics of Materials and Structures, 4 (2009), 139-156. |
[20] |
G. Del Piero and L. Deseri, On the concepts of state and free energy in linear viscoelasticity, Archive for Rational Mechanics and Analysis, 138 (1997), 1-35.
doi: 10.1007/s002050050035. |
[21] |
L. Deseri, M. Fabrizio and M. Golden, The concept of a minimal state in viscoelasticity: New free energies and applications to PDEs, Archive for Rational Mechanics and Analysis, 181 (2006), 43-96.
doi: 10.1007/s00205-005-0406-1. |
[22] |
M. Di Paola and M. Zingales, Exact mechanical models for fractional viscoelastic material, Journal of Rheology, 56 (2012), 983-1004. |
[23] |
M. Di Paola and M. Zingales, A discrete mechanical model of fractional hereditary materials, Meccanica, 48 (2013), 1573-1586.
doi: 10.1007/s11012-012-9685-4. |
[24] |
M. Fabrizio, C. Giorgi and A. Morro, Free energies and dissipation properties for systems with memory, Archive for Rational Mechanics and Analysis, 125 (1994), 341-373. |
[25] |
M. Fabrizio and B. Lazzari, On the existence and the asymptotic stability of solutions for linearly viscoelastic solids, Archive for Rational Mechanics and Analysis, 116 (1991), 139-152.
doi: 10.1007/BF00375589. |
[26] |
M. Fabrizio and A. Morro, Mathematical Problems in Linear Viscoelasticity, SIAM, Philadelphia, 1992.
doi: 10.1137/1.9781611970807. |
[27] |
D. Graffi and M. Fabrizio, Sulla nozione di stato per materiali viscoelastici di tipo "rate", Atti Acc. Lincei, Rend. Fis., 83 (1989), 201-208. |
[28] |
L. Hörmander, The Analysis of Linear Partial Differential Operators I: Differential Operators with Constant Coefficients, Grundlehren der mathematischen Wissenschaften, 1998.
doi: 10.1007/978-3-642-96750-4. |
[29] |
D. Ieşan, On the theory of viscoelastic mixtures, Journal of Thermal Stresses, 27 (2004), 1125-1148.
doi: 10.1080/01495730490498575. |
[30] |
D. Ieşan, A theory of thermoviscoelastic composites modelled as interacting Cosserat continua, Journal of Thermal Stresses, 30 (2007), 1269-1289. |
[31] |
D. Ieşan, On a theory of thermoviscoelastic materials with voids, Journal of Elasticity, 104 (2011), 369-384.
doi: 10.1007/s10659-010-9300-7. |
[32] |
D. Ieşan and L. Nappa, On the theory of viscoelastic mixtures and stability, Mathematics and Mechanics of Solids, 13 (2008), 55-80.
doi: 10.1177/1081286506072351. |
[33] |
R. Lakes, Viscoelastic Materials, Cambridge University Press, Cambridge, New York, Melbourne, 2009.
doi: 10.1017/CBO9780511626722. |
[34] |
M. Y. Khaled, D. E. Beskos and E. C. Aifantis, On the theory of consolidation with double porosity - III, International Journal for Numerical and Analytical Methods in Geomechanics, 8 (1984), 101-123. |
[35] |
N. Khalili, Coupling effects in double porosity media with deformable matrix, Geophysical Research Letters, 30 (2003), 2153.
doi: 10.1029/2003GL018544. |
[36] |
N. Khalili and S. Valliappan, Unified theory of flow and deformation in double porous media, European Journal of Mechanics - A/Solids, 15 (1996), 321-336. |
[37] |
F. Martínez and R. Quintanilla, Existence, uniqueness and asymptotic behaviour of solutions to the equations of viscoelasticity with voids, International Journal of Solids and Structures, 35 (1998), 3347-3361.
doi: 10.1016/S0020-7683(98)00018-3. |
[38] |
F. Passarella, V. Tibullo and V. Zampoli, On microstretch thermoviscoelastic composite materials, Europ. J. Mechanics, A/Solids, 37 (2013), 294-303.
doi: 10.1016/j.euromechsol.2012.07.002. |
[39] |
S. R. Pride and J. G. Berryman, Linear dynamics of double-porosity dual-permeability materials - I, Physical Review E, 68 (2003), 036603.
doi: 10.1103/PhysRevE.68.036603. |
[40] |
R. Quintanilla, Existence and exponential decay in the linear theory of viscoelastic mixtures, European Journal of Mechanics A/Solids, 24 (2005), 311-324.
doi: 10.1016/j.euromechsol.2004.11.008. |
[41] |
E. Rohan, S. Naili, R. Cimrman and T. Lemaire, Multiscale modeling of a fluid saturated medium with double porosity: Relevance to the compact bone, Journal of the Mechanics and Physics of Solids, 60 (2012), 857-881.
doi: 10.1016/j.jmps.2012.01.013. |
[42] |
A. Scalia, Shock waves in viscoelastic materials with voids, Wave Motion, 19 (1994), 125-133.
doi: 10.1016/0165-2125(94)90061-2. |
[43] |
K. Sharma and P. Kumar, Propagation of plane waves and fundamental solution in thermoviscoelastic medium with voids, Journal of Thermal Stresses, 36 (2013), 94-111.
doi: 10.1080/01495739.2012.720545. |
[44] |
B. Straughan, Stability and uniqueness in double porosity elasticity, International Journal of Engineering Science, 65 (2013), 1-8.
doi: 10.1016/j.ijengsci.2013.01.001. |
[45] |
M. M. Svanadze, Potential method in the linear theories of viscoelasticity and thermoviscoelasticity for Kelvin-Voigt materials, Technische Mechanik, 32 (2012), 554-563. |
[46] |
M. M. Svanadze, Potential method in the linear theory of viscoelastic materials with voids, Journal of Elasticity, 114 (2014), 101-126.
doi: 10.1007/s10659-013-9429-2. |
[47] |
M. M. Svanadze, On the solutions of equations of the linear thermoviscoelasticity theory for Kelvin-Voigt materials with voids, Journal of Thermal Stresses, 37 (2014), 253-269.
doi: 10.1080/01495739.2013.839851. |
[48] |
M. Svanadze, Fundamental solution in the theory of consolidation with double porosity, Journal of the Mechanical Behavior of Materials, 16 (2005), 123-130.
doi: 10.1515/JMBM.2005.16.1-2.123. |
[49] |
M. Svanadze, Plane waves and boundary value problems in the theory of elasticity for solids with double porosity, Acta Applicandae Mathematicae, 122 (2012), 461-471.
doi: 10.1007/s10440-012-9756-5. |
[50] |
M. Svanadze, The boundary value problems of the full coupled theory of poroelasticity for materials with double porosity, Proceedings in Applied Mathematics and Mechanics, 12 (2012), 279-282.
doi: 10.1002/pamm.201210130. |
[51] |
M. Svanadze, Fundamental solution in the linear theory of consolidation for elastic solids with double porosity, Journal of Mathematical Sciciences, 195 (2013), 258-268.
doi: 10.1007/s10958-013-1578-0. |
[52] |
M. Svanadze and S. De Cicco, Fundamental solutions in the full coupled linear theory of elasticity for solid with double porosity, Archives of Mechanics, 65 (2013), 367-390. |
[53] |
M. Svanadze and G. Iovane, Fundamental solution in the linear theory of thermoviscoelastic mixtures, European Journal of Applied Mathematics, 18 (2007), 323-335.
doi: 10.1017/S0956792507006961. |
[54] |
M. Svanadze and A. Scalia, Mathematical problems in the coupled linear theory of bone poroelasticity, Computers and Mathematics with Applications, 66 (2013), 1554-1566.
doi: 10.1016/j.camwa.2013.01.046. |
[55] |
R. K. Wilson and E. C. Aifantis, On the theory of consolidation with double porosity - I, International Journal of Engineering Science, 20 (1982), 1009-1035. |
[56] |
Y. Zhao and M. Chen, Fully coupled dual-porosity model for anisotropic formations, International Journal of Rock Mechanics and Mining Sciences, 43 (2006), 1128-1133.
doi: 10.1016/j.ijrmms.2006.03.001. |
show all references
References:
[1] |
G. Amendola, M. Fabrizio and J. M. Golden, Thermodynamics of Materials with Memory: Theory and Applications, Springer, New York, Dordrecht, Heidelberg, London, 2012.
doi: 10.1007/978-1-4614-1692-0. |
[2] |
J. A. D. Appleby, M. Fabrizio, B. Lazzari and D. W. Reynolds, On exponential asymptotic stability in linear viscoelasticity, Mathematical Models and Methods in Applied Sciences, 16 (2006), 1677-1694.
doi: 10.1142/S0218202506001674. |
[3] |
G. I. Barenblatt, I. P. Zheltov and I. N. Kochina, Basic concept in the theory of seepage of homogeneous liquids in fissured rocks (strata), Journal of Applied Mathematics and Mechanics, 24 (1960), 1286-1303.
doi: 10.1016/0021-8928(60)90107-6. |
[4] |
J. G. Berryman and H. F. Wang, The elastic coefficients of double-porosity models for fluid transport in jointed rock, Journal of Geophysical Research, 100 (1995), 24611-24627.
doi: 10.1029/95JB02161. |
[5] |
J. G. Berryman and H. F. Wang, Elastic wave propagation and attenuation in a double-porosity dual-permiability medium, International Journal of Rock Mechanics and Mining Sciences, 37 (2000), 63-78.
doi: 10.1016/S1365-1609(99)00092-1. |
[6] |
D. E. Beskos and E. C. Aifantis, On the theory of consolidation with double porosity - II, International Journal of Engineering Science, 24 (1986), 1697-1716.
doi: 10.1016/0020-7225(86)90076-5. |
[7] |
M. A. Biot, General theory of three-dimensional consolidation, Journal of Applied Physics, 12 (1941), 155-164.
doi: 10.1063/1.1712886. |
[8] |
M. A. Biot, Theory of propagation of elastic waves in a fluid-saturated porous solid, I. Low frequency range, II. Higher frequency range, Journal of the Acoustical Society of America, 28 (1956), 179-191.
doi: 10.1121/1.1908241. |
[9] |
M. A. Biot, Mechanics of deformation and acoustic propagation in porous media, Journal of Applied Physics, 33 (1962), 1482-1498.
doi: 10.1063/1.1728759. |
[10] |
M. A. Biot, Theory of finite deformations of porous solids, Indiana University Mathematics Journal, 21 (1972), 597-620. |
[11] |
S. Chiriţă, C. Galeş and I. D. Ghiba, On spatial behavior of the harmonic vibrations in Kelvin-Voigt materials, Journal of Elasticity, 93 (2008), 81-92.
doi: 10.1007/s10659-008-9167-z. |
[12] |
R. M. Christensen, Theory of Viscoelasticity, 2nd ed., Dover Publ. Inc., Mineola, New York, 2010. |
[13] |
M. Ciarletta, F. Passarella and M. Svanadze, Plane waves and uniqueness theorems in the coupled linear theory of elasticity for solids with double porosity, Journal of Elasticity, 114 (2014), 55-68.
doi: 10.1007/s10659-012-9426-x. |
[14] |
M. Ciarletta and A. Scalia, On some theorems in the linear theory of viscoelastic materials with voids, Journal of Elasticity, 25 (1991), 149-158.
doi: 10.1007/BF00042463. |
[15] |
S. C. Cowin, The viscoelastic behavior of linear elastic materials with voids, Journal of Elasticity, 15 (1985), 185-191.
doi: 10.1007/BF00041992. |
[16] |
S. C. Cowin, Bone poroelasticity, Journal of Biomechanics, 32 (1999), 217-238.
doi: 10.1016/S0021-9290(98)00161-4. |
[17] |
S. C. Cowin, G. Gailani and M. Benalla, Hierarchical poroelasticity: Movement of interstitial fluid between levels in bones, Philosophical Transactions of the Royal Society A: mathematical, physical and engineering sciences, 367 (2009), 3401-3444.
doi: 10.1098/rsta.2009.0099. |
[18] |
S. De Cicco and L. Nappa, Singular surfaces in thermoviscoelastic materials with voids, Journal of Elasticity, 73 (2003), 191-210.
doi: 10.1023/B:ELAS.0000029961.09749.2b. |
[19] |
S. De Cicco and M. Svanadze, Fundamental solution in the theory of viscoelastic mixtures, Journal of Mechanics of Materials and Structures, 4 (2009), 139-156. |
[20] |
G. Del Piero and L. Deseri, On the concepts of state and free energy in linear viscoelasticity, Archive for Rational Mechanics and Analysis, 138 (1997), 1-35.
doi: 10.1007/s002050050035. |
[21] |
L. Deseri, M. Fabrizio and M. Golden, The concept of a minimal state in viscoelasticity: New free energies and applications to PDEs, Archive for Rational Mechanics and Analysis, 181 (2006), 43-96.
doi: 10.1007/s00205-005-0406-1. |
[22] |
M. Di Paola and M. Zingales, Exact mechanical models for fractional viscoelastic material, Journal of Rheology, 56 (2012), 983-1004. |
[23] |
M. Di Paola and M. Zingales, A discrete mechanical model of fractional hereditary materials, Meccanica, 48 (2013), 1573-1586.
doi: 10.1007/s11012-012-9685-4. |
[24] |
M. Fabrizio, C. Giorgi and A. Morro, Free energies and dissipation properties for systems with memory, Archive for Rational Mechanics and Analysis, 125 (1994), 341-373. |
[25] |
M. Fabrizio and B. Lazzari, On the existence and the asymptotic stability of solutions for linearly viscoelastic solids, Archive for Rational Mechanics and Analysis, 116 (1991), 139-152.
doi: 10.1007/BF00375589. |
[26] |
M. Fabrizio and A. Morro, Mathematical Problems in Linear Viscoelasticity, SIAM, Philadelphia, 1992.
doi: 10.1137/1.9781611970807. |
[27] |
D. Graffi and M. Fabrizio, Sulla nozione di stato per materiali viscoelastici di tipo "rate", Atti Acc. Lincei, Rend. Fis., 83 (1989), 201-208. |
[28] |
L. Hörmander, The Analysis of Linear Partial Differential Operators I: Differential Operators with Constant Coefficients, Grundlehren der mathematischen Wissenschaften, 1998.
doi: 10.1007/978-3-642-96750-4. |
[29] |
D. Ieşan, On the theory of viscoelastic mixtures, Journal of Thermal Stresses, 27 (2004), 1125-1148.
doi: 10.1080/01495730490498575. |
[30] |
D. Ieşan, A theory of thermoviscoelastic composites modelled as interacting Cosserat continua, Journal of Thermal Stresses, 30 (2007), 1269-1289. |
[31] |
D. Ieşan, On a theory of thermoviscoelastic materials with voids, Journal of Elasticity, 104 (2011), 369-384.
doi: 10.1007/s10659-010-9300-7. |
[32] |
D. Ieşan and L. Nappa, On the theory of viscoelastic mixtures and stability, Mathematics and Mechanics of Solids, 13 (2008), 55-80.
doi: 10.1177/1081286506072351. |
[33] |
R. Lakes, Viscoelastic Materials, Cambridge University Press, Cambridge, New York, Melbourne, 2009.
doi: 10.1017/CBO9780511626722. |
[34] |
M. Y. Khaled, D. E. Beskos and E. C. Aifantis, On the theory of consolidation with double porosity - III, International Journal for Numerical and Analytical Methods in Geomechanics, 8 (1984), 101-123. |
[35] |
N. Khalili, Coupling effects in double porosity media with deformable matrix, Geophysical Research Letters, 30 (2003), 2153.
doi: 10.1029/2003GL018544. |
[36] |
N. Khalili and S. Valliappan, Unified theory of flow and deformation in double porous media, European Journal of Mechanics - A/Solids, 15 (1996), 321-336. |
[37] |
F. Martínez and R. Quintanilla, Existence, uniqueness and asymptotic behaviour of solutions to the equations of viscoelasticity with voids, International Journal of Solids and Structures, 35 (1998), 3347-3361.
doi: 10.1016/S0020-7683(98)00018-3. |
[38] |
F. Passarella, V. Tibullo and V. Zampoli, On microstretch thermoviscoelastic composite materials, Europ. J. Mechanics, A/Solids, 37 (2013), 294-303.
doi: 10.1016/j.euromechsol.2012.07.002. |
[39] |
S. R. Pride and J. G. Berryman, Linear dynamics of double-porosity dual-permeability materials - I, Physical Review E, 68 (2003), 036603.
doi: 10.1103/PhysRevE.68.036603. |
[40] |
R. Quintanilla, Existence and exponential decay in the linear theory of viscoelastic mixtures, European Journal of Mechanics A/Solids, 24 (2005), 311-324.
doi: 10.1016/j.euromechsol.2004.11.008. |
[41] |
E. Rohan, S. Naili, R. Cimrman and T. Lemaire, Multiscale modeling of a fluid saturated medium with double porosity: Relevance to the compact bone, Journal of the Mechanics and Physics of Solids, 60 (2012), 857-881.
doi: 10.1016/j.jmps.2012.01.013. |
[42] |
A. Scalia, Shock waves in viscoelastic materials with voids, Wave Motion, 19 (1994), 125-133.
doi: 10.1016/0165-2125(94)90061-2. |
[43] |
K. Sharma and P. Kumar, Propagation of plane waves and fundamental solution in thermoviscoelastic medium with voids, Journal of Thermal Stresses, 36 (2013), 94-111.
doi: 10.1080/01495739.2012.720545. |
[44] |
B. Straughan, Stability and uniqueness in double porosity elasticity, International Journal of Engineering Science, 65 (2013), 1-8.
doi: 10.1016/j.ijengsci.2013.01.001. |
[45] |
M. M. Svanadze, Potential method in the linear theories of viscoelasticity and thermoviscoelasticity for Kelvin-Voigt materials, Technische Mechanik, 32 (2012), 554-563. |
[46] |
M. M. Svanadze, Potential method in the linear theory of viscoelastic materials with voids, Journal of Elasticity, 114 (2014), 101-126.
doi: 10.1007/s10659-013-9429-2. |
[47] |
M. M. Svanadze, On the solutions of equations of the linear thermoviscoelasticity theory for Kelvin-Voigt materials with voids, Journal of Thermal Stresses, 37 (2014), 253-269.
doi: 10.1080/01495739.2013.839851. |
[48] |
M. Svanadze, Fundamental solution in the theory of consolidation with double porosity, Journal of the Mechanical Behavior of Materials, 16 (2005), 123-130.
doi: 10.1515/JMBM.2005.16.1-2.123. |
[49] |
M. Svanadze, Plane waves and boundary value problems in the theory of elasticity for solids with double porosity, Acta Applicandae Mathematicae, 122 (2012), 461-471.
doi: 10.1007/s10440-012-9756-5. |
[50] |
M. Svanadze, The boundary value problems of the full coupled theory of poroelasticity for materials with double porosity, Proceedings in Applied Mathematics and Mechanics, 12 (2012), 279-282.
doi: 10.1002/pamm.201210130. |
[51] |
M. Svanadze, Fundamental solution in the linear theory of consolidation for elastic solids with double porosity, Journal of Mathematical Sciciences, 195 (2013), 258-268.
doi: 10.1007/s10958-013-1578-0. |
[52] |
M. Svanadze and S. De Cicco, Fundamental solutions in the full coupled linear theory of elasticity for solid with double porosity, Archives of Mechanics, 65 (2013), 367-390. |
[53] |
M. Svanadze and G. Iovane, Fundamental solution in the linear theory of thermoviscoelastic mixtures, European Journal of Applied Mathematics, 18 (2007), 323-335.
doi: 10.1017/S0956792507006961. |
[54] |
M. Svanadze and A. Scalia, Mathematical problems in the coupled linear theory of bone poroelasticity, Computers and Mathematics with Applications, 66 (2013), 1554-1566.
doi: 10.1016/j.camwa.2013.01.046. |
[55] |
R. K. Wilson and E. C. Aifantis, On the theory of consolidation with double porosity - I, International Journal of Engineering Science, 20 (1982), 1009-1035. |
[56] |
Y. Zhao and M. Chen, Fully coupled dual-porosity model for anisotropic formations, International Journal of Rock Mechanics and Mining Sciences, 43 (2006), 1128-1133.
doi: 10.1016/j.ijrmms.2006.03.001. |
[1] |
Ali Wehbe, Rayan Nasser, Nahla Noun. Stability of N-D transmission problem in viscoelasticity with localized Kelvin-Voigt damping under different types of geometric conditions. Mathematical Control and Related Fields, 2021, 11 (4) : 885-904. doi: 10.3934/mcrf.2020050 |
[2] |
Miroslav Bulíček, Josef Málek, K. R. Rajagopal. On Kelvin-Voigt model and its generalizations. Evolution Equations and Control Theory, 2012, 1 (1) : 17-42. doi: 10.3934/eect.2012.1.17 |
[3] |
Louis Tebou. Stabilization of some elastodynamic systems with localized Kelvin-Voigt damping. Discrete and Continuous Dynamical Systems, 2016, 36 (12) : 7117-7136. doi: 10.3934/dcds.2016110 |
[4] |
Mikhail Turbin, Anastasiia Ustiuzhaninova. Pullback attractors for weak solution to modified Kelvin-Voigt model. Evolution Equations and Control Theory, 2022 doi: 10.3934/eect.2022011 |
[5] |
Ahmed Bchatnia, Nadia Souayeh. Eventual differentiability of coupled wave equations with local Kelvin-Voigt damping. Discrete and Continuous Dynamical Systems - S, 2022, 15 (6) : 1317-1338. doi: 10.3934/dcdss.2022098 |
[6] |
Fathi Hassine. Asymptotic behavior of the transmission Euler-Bernoulli plate and wave equation with a localized Kelvin-Voigt damping. Discrete and Continuous Dynamical Systems - B, 2016, 21 (6) : 1757-1774. doi: 10.3934/dcdsb.2016021 |
[7] |
Xiaobin Yao, Qiaozhen Ma, Tingting Liu. Asymptotic behavior for stochastic plate equations with rotational inertia and Kelvin-Voigt dissipative term on unbounded domains. Discrete and Continuous Dynamical Systems - B, 2019, 24 (4) : 1889-1917. doi: 10.3934/dcdsb.2018247 |
[8] |
Serge Nicaise, Cristina Pignotti. Stability of the wave equation with localized Kelvin-Voigt damping and boundary delay feedback. Discrete and Continuous Dynamical Systems - S, 2016, 9 (3) : 791-813. doi: 10.3934/dcdss.2016029 |
[9] |
Robert E. Miller. Homogenization of time-dependent systems with Kelvin-Voigt damping by two-scale convergence. Discrete and Continuous Dynamical Systems, 1995, 1 (4) : 485-502. doi: 10.3934/dcds.1995.1.485 |
[10] |
Manil T. Mohan. On the three dimensional Kelvin-Voigt fluids: global solvability, exponential stability and exact controllability of Galerkin approximations. Evolution Equations and Control Theory, 2020, 9 (2) : 301-339. doi: 10.3934/eect.2020007 |
[11] |
Manil T. Mohan. Global attractors, exponential attractors and determining modes for the three dimensional Kelvin-Voigt fluids with "fading memory". Evolution Equations and Control Theory, 2022, 11 (1) : 125-167. doi: 10.3934/eect.2020105 |
[12] |
Zhong-Jie Han, Zhuangyi Liu, Jing Wang. Sharper and finer energy decay rate for an elastic string with localized Kelvin-Voigt damping. Discrete and Continuous Dynamical Systems - S, 2022, 15 (6) : 1455-1467. doi: 10.3934/dcdss.2022031 |
[13] |
Mohammad Akil, Ibtissam Issa, Ali Wehbe. Energy decay of some boundary coupled systems involving wave\ Euler-Bernoulli beam with one locally singular fractional Kelvin-Voigt damping. Mathematical Control and Related Fields, 2021 doi: 10.3934/mcrf.2021059 |
[14] |
Victor Zvyagin, Vladimir Orlov. Weak solvability of fractional Voigt model of viscoelasticity. Discrete and Continuous Dynamical Systems, 2018, 38 (12) : 6327-6350. doi: 10.3934/dcds.2018270 |
[15] |
Brahim Amaziane, Mladen Jurak, Leonid Pankratov, Anja Vrbaški. Some remarks on the homogenization of immiscible incompressible two-phase flow in double porosity media. Discrete and Continuous Dynamical Systems - B, 2018, 23 (2) : 629-665. doi: 10.3934/dcdsb.2018037 |
[16] |
Manil T. Mohan. Global and exponential attractors for the 3D Kelvin-Voigt-Brinkman-Forchheimer equations. Discrete and Continuous Dynamical Systems - B, 2020, 25 (9) : 3393-3436. doi: 10.3934/dcdsb.2020067 |
[17] |
Jacobo Baldonedo, José R. Fernández, Ramón Quintanilla. On the time decay for the MGT-type porosity problems. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022009 |
[18] |
Francesco Maddalena, Danilo Percivale, Franco Tomarelli. Adhesive flexible material structures. Discrete and Continuous Dynamical Systems - B, 2012, 17 (2) : 553-574. doi: 10.3934/dcdsb.2012.17.553 |
[19] |
Yasemin Şengül. Viscoelasticity with limiting strain. Discrete and Continuous Dynamical Systems - S, 2021, 14 (1) : 57-70. doi: 10.3934/dcdss.2020330 |
[20] |
Toyohiko Aiki. A free boundary problem for an elastic material. Conference Publications, 2007, 2007 (Special) : 10-17. doi: 10.3934/proc.2007.2007.10 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]