-
Previous Article
A short course on numerical simulation of viscous flow: Discretization, optimization and stability analysis
- DCDS-S Home
- This Issue
-
Next Article
Stability and interaction of vortices in two-dimensional viscous flows
The thermo-mechanics of rate-type fluids
1. | Department of Mechanical Engineering, Texas A&M University, College Station, TX-77843, United States |
References:
[1] |
G. Barot, I. J. Rao and K. R. Rajagopal, A thermodynamic framework for the modeling of crystallizable shape memory polymers,, International Journal of Engineering Science, 46 (2008), 325.
doi: 10.1016/j.ijengsci.2007.11.008. |
[2] |
A. N. Beris and S. F. Edwards, "Thermodynamics of Flowing Systems with Internal Microstructure,", Oxford Engineering Science Series 36, (1994).
|
[3] |
D. R. Bland, "The Linear Theory of Viscoelasticity,", Pergamon Press, (1960).
|
[4] |
J. M. Burgers, "Mechanical Considerations-model Systems-Phenomenological Theories of Relaxation and Viscosity,", In: First Report on Viscosity and Plasticity, (1939). Google Scholar |
[5] |
A. L. Cauchy, Recherches sur lequilibre et le mouvement interieur des corps solides ou fluids, elastiques ou non elastiques,, Bull. Soc. Philomath, (1823), 9. Google Scholar |
[6] |
J. D. Ferry, "Viscoelastic Properties of Polymers,", Wiley, (1980). Google Scholar |
[7] |
J. Finger, Über die allgemeisten Bezeihungen zwischen Deformationen und den zugehoringen Spannungenin aelotropen und isotropen substanzen,, Akad. Wiss. Wien Sitzungsber, 103 (1894), 1073. Google Scholar |
[8] |
G. Green, On the laws of reflexion and refraction of light at the common surface of two non-crystallized media,, (1837), (1837), 1839. Google Scholar |
[9] |
A. E. Green and P. M. Naghdi, On thermodynamics and nature of second law,, Proc. Roy. Soc. Lond. A, 357 (1977), 253.
doi: 10.1098/rspa.1977.0166. |
[10] |
M. Heida and J. Málek, On Korteweg-type compressible fluid-like materials,, International Journal of Engineering Science, 48 (2010), 1313.
doi: 10.1016/j.ijengsci.2010.06.031. |
[11] |
M. Heida, J. Málek and K. R. Rajagopal, On the development and generalizations of Cahn-Hilliard equations within a thermodynamic framework,, Zeitschrift für Angewandte Mathematik und Physik, 63 (2012), 145. Google Scholar |
[12] |
M. Heida, J. Málek and K. R. Rajagopal, On the development and generalizations of Allen-Cahn and Stefan equations within a thermodynamic framework,, Zeitschrift für Angewandte Mathematik und Physik, (2012). Google Scholar |
[13] |
K. Kannan and K. R. Rajagopal, A thermodynamic framework for chemically reacting systems,, Zeitschrift für Angewandte Mathematik und Physik, 62 (2011), 331.
|
[14] |
J. M. Krishnan and K. R. Rajagopal, On the mechanical behavior of asphalt,, Mech. of Materials, 37 (2005), 1085.
doi: 10.1016/j.mechmat.2004.09.005. |
[15] |
J. Málek and K. R. Rajagopal, Incompressible rate type fluids with pressure and shear-rate dependent material moduli,, Nonlinear Anal. Real World Appl., 8 (2007), 156.
doi: 10.1016/j.nonrwa.2005.06.006. |
[16] |
J. Málek and K. R. Rajagopal, A thermodynamic framework for a mixture of two liquids, 2008, Nonlinear Anal. Real World Appl., 9 (2008), 1649.
doi: 10.1016/j.nonrwa.2007.04.008. |
[17] |
J. C. Maxwell, On the dynamical theory of gases,, Philosophical Transactions of the Royal Society, 157 (1866), 26. Google Scholar |
[18] |
W. Noll, On the foundations of mechanics of continuous media,, Carnegie Institute of Technology, (1957). Google Scholar |
[19] |
J. G. Oldroyd, On the formulation of the rheological equations of state,, Proc. Roy. Soc. Lond. A, 200 (1950), 523.
doi: 10.1098/rspa.1950.0035. |
[20] |
S. C. Prasad, K. R. Rajagopal and I. J. Rao, A continuum model for the creep of single crystal nickel-base superalloys,, Acta Mater., 53 (2005), 669.
doi: 10.1016/j.actamat.2004.10.020. |
[21] |
S. C. Prasad, K. R. Rajagopal and I. J. Rao, A continuum model for the anisotropic creep of single crystal nickel-based superalloys,, Acta Mater., 54 (2006), 1487.
doi: 10.1016/j.actamat.2005.11.016. |
[22] |
K. R. Rajagopal and A. R. Srinivasa, On the inelastic behavior of solids - Part 1: Twinning,, Int. J. Plast., 11 (1995), 653.
doi: 10.1016/S0749-6419(95)00027-5. |
[23] |
K. R. Rajagopal and A. R. Srinivasa, Inelastic behavior of materials - part II: Energetics associated with discontinuous twinning,, Int. J. Plast., 13 (1997), 1.
doi: 10.1016/S0749-6419(96)00049-6. |
[24] |
K. R. Rajagopal and A. R. Srinivasa, Mechanics of the inelastic behavior of materials - part I: Theoretical underpinnings,, Int. J. Plast., 14) (1998), 945. Google Scholar |
[25] |
K. R. Rajagopal and A. R. Srinivasa, Mechanics of the inelastic behavior of materials - part II: Inelastic response,, Int. J. Plast., 14) (1998), 969. Google Scholar |
[26] |
K. R. Rajagopal and A. R. Srinivasa, On the thermomechanics of shape memory wires,, Zeitschrift für Angewandte Mathematik und Physik, 50 (1999), 459.
|
[27] |
K. R. Rajagopal and A. R. Srinivasa, Thermodynamics of Rate type fluid model,, Journal of Non-Newtonian Fluid Mechanics, 88 (2000), 207.
doi: 10.1016/S0377-0257(99)00023-3. |
[28] |
K. R. Rajagopal and A. R. Srinivasa, Modeling anisotropic fluids within the framework of bodies with multiple natural configurations,, Journal of Non-Newtonian Fluid Mechanics, 99 (2001), 109.
doi: 10.1016/S0377-0257(01)00116-1. |
[29] |
K. R. Rajagopal and A. R. Srinivasa, On the thermomechanics of materials that have multiple natural configurations - part I: Viscoelasticity and classical plasticity,, Zeitschrift für Angewandte Mathematik und Physik, 55 (2004), 861.
|
[30] |
K. R. Rajagopal and A. R. Srinivasa, On the thermomechanics of materials that have multiple natural configurations - part II: Twinning and solid to solid phase transformation,, Zeitschrift für Angewandte Mathematik und Physik, 55 (2004), 1074.
|
[31] |
K. R. Rajagopal and A. R. Srinivasa, On the response of non-dissipative solids,, Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci., 463 (2007), 357.
|
[32] |
K. R. Rajagopal and A. R. Srinivasa, On a class of non-dissipative materials that are not hyperelastic,, Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci., 465 (2009), 495.
|
[33] |
K. R. Rajagopal and A. R. Srinivasa, A Gibbs-potential-based formulation for obtaining the response functions for a class of viscoelastic materials,, Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci., 467 (2011), 39.
|
[34] |
K. R. Rajagopal and A. R. Srinivasa, "Restrictions Placed on Constitutive Relations by Angular Momentum Balance and Galilean Invariance,", In Press, (2012). Google Scholar |
[35] |
K. R. Rajagopal and A. S. Wineman, "Mechanical Response of Polymers,", Cambridge University Press, (2001). Google Scholar |
[36] |
I. J. Rao and K. R. Rajagopal, A thermodynamic framework for the study of crystallization in polymers,, Zeitschrift für Angewandte Mathematik und Physik, 53 (2002), 365.
|
[37] |
C. Truesdell, Mechanical Foundations of Elasticity and Fluid Dynamics,, Mechanics I, (1966), 125. Google Scholar |
[38] |
C. Truesdell and W. Noll, "Non-Linear Field Theories of Mechanics,", 2nd edition, (1992).
|
show all references
References:
[1] |
G. Barot, I. J. Rao and K. R. Rajagopal, A thermodynamic framework for the modeling of crystallizable shape memory polymers,, International Journal of Engineering Science, 46 (2008), 325.
doi: 10.1016/j.ijengsci.2007.11.008. |
[2] |
A. N. Beris and S. F. Edwards, "Thermodynamics of Flowing Systems with Internal Microstructure,", Oxford Engineering Science Series 36, (1994).
|
[3] |
D. R. Bland, "The Linear Theory of Viscoelasticity,", Pergamon Press, (1960).
|
[4] |
J. M. Burgers, "Mechanical Considerations-model Systems-Phenomenological Theories of Relaxation and Viscosity,", In: First Report on Viscosity and Plasticity, (1939). Google Scholar |
[5] |
A. L. Cauchy, Recherches sur lequilibre et le mouvement interieur des corps solides ou fluids, elastiques ou non elastiques,, Bull. Soc. Philomath, (1823), 9. Google Scholar |
[6] |
J. D. Ferry, "Viscoelastic Properties of Polymers,", Wiley, (1980). Google Scholar |
[7] |
J. Finger, Über die allgemeisten Bezeihungen zwischen Deformationen und den zugehoringen Spannungenin aelotropen und isotropen substanzen,, Akad. Wiss. Wien Sitzungsber, 103 (1894), 1073. Google Scholar |
[8] |
G. Green, On the laws of reflexion and refraction of light at the common surface of two non-crystallized media,, (1837), (1837), 1839. Google Scholar |
[9] |
A. E. Green and P. M. Naghdi, On thermodynamics and nature of second law,, Proc. Roy. Soc. Lond. A, 357 (1977), 253.
doi: 10.1098/rspa.1977.0166. |
[10] |
M. Heida and J. Málek, On Korteweg-type compressible fluid-like materials,, International Journal of Engineering Science, 48 (2010), 1313.
doi: 10.1016/j.ijengsci.2010.06.031. |
[11] |
M. Heida, J. Málek and K. R. Rajagopal, On the development and generalizations of Cahn-Hilliard equations within a thermodynamic framework,, Zeitschrift für Angewandte Mathematik und Physik, 63 (2012), 145. Google Scholar |
[12] |
M. Heida, J. Málek and K. R. Rajagopal, On the development and generalizations of Allen-Cahn and Stefan equations within a thermodynamic framework,, Zeitschrift für Angewandte Mathematik und Physik, (2012). Google Scholar |
[13] |
K. Kannan and K. R. Rajagopal, A thermodynamic framework for chemically reacting systems,, Zeitschrift für Angewandte Mathematik und Physik, 62 (2011), 331.
|
[14] |
J. M. Krishnan and K. R. Rajagopal, On the mechanical behavior of asphalt,, Mech. of Materials, 37 (2005), 1085.
doi: 10.1016/j.mechmat.2004.09.005. |
[15] |
J. Málek and K. R. Rajagopal, Incompressible rate type fluids with pressure and shear-rate dependent material moduli,, Nonlinear Anal. Real World Appl., 8 (2007), 156.
doi: 10.1016/j.nonrwa.2005.06.006. |
[16] |
J. Málek and K. R. Rajagopal, A thermodynamic framework for a mixture of two liquids, 2008, Nonlinear Anal. Real World Appl., 9 (2008), 1649.
doi: 10.1016/j.nonrwa.2007.04.008. |
[17] |
J. C. Maxwell, On the dynamical theory of gases,, Philosophical Transactions of the Royal Society, 157 (1866), 26. Google Scholar |
[18] |
W. Noll, On the foundations of mechanics of continuous media,, Carnegie Institute of Technology, (1957). Google Scholar |
[19] |
J. G. Oldroyd, On the formulation of the rheological equations of state,, Proc. Roy. Soc. Lond. A, 200 (1950), 523.
doi: 10.1098/rspa.1950.0035. |
[20] |
S. C. Prasad, K. R. Rajagopal and I. J. Rao, A continuum model for the creep of single crystal nickel-base superalloys,, Acta Mater., 53 (2005), 669.
doi: 10.1016/j.actamat.2004.10.020. |
[21] |
S. C. Prasad, K. R. Rajagopal and I. J. Rao, A continuum model for the anisotropic creep of single crystal nickel-based superalloys,, Acta Mater., 54 (2006), 1487.
doi: 10.1016/j.actamat.2005.11.016. |
[22] |
K. R. Rajagopal and A. R. Srinivasa, On the inelastic behavior of solids - Part 1: Twinning,, Int. J. Plast., 11 (1995), 653.
doi: 10.1016/S0749-6419(95)00027-5. |
[23] |
K. R. Rajagopal and A. R. Srinivasa, Inelastic behavior of materials - part II: Energetics associated with discontinuous twinning,, Int. J. Plast., 13 (1997), 1.
doi: 10.1016/S0749-6419(96)00049-6. |
[24] |
K. R. Rajagopal and A. R. Srinivasa, Mechanics of the inelastic behavior of materials - part I: Theoretical underpinnings,, Int. J. Plast., 14) (1998), 945. Google Scholar |
[25] |
K. R. Rajagopal and A. R. Srinivasa, Mechanics of the inelastic behavior of materials - part II: Inelastic response,, Int. J. Plast., 14) (1998), 969. Google Scholar |
[26] |
K. R. Rajagopal and A. R. Srinivasa, On the thermomechanics of shape memory wires,, Zeitschrift für Angewandte Mathematik und Physik, 50 (1999), 459.
|
[27] |
K. R. Rajagopal and A. R. Srinivasa, Thermodynamics of Rate type fluid model,, Journal of Non-Newtonian Fluid Mechanics, 88 (2000), 207.
doi: 10.1016/S0377-0257(99)00023-3. |
[28] |
K. R. Rajagopal and A. R. Srinivasa, Modeling anisotropic fluids within the framework of bodies with multiple natural configurations,, Journal of Non-Newtonian Fluid Mechanics, 99 (2001), 109.
doi: 10.1016/S0377-0257(01)00116-1. |
[29] |
K. R. Rajagopal and A. R. Srinivasa, On the thermomechanics of materials that have multiple natural configurations - part I: Viscoelasticity and classical plasticity,, Zeitschrift für Angewandte Mathematik und Physik, 55 (2004), 861.
|
[30] |
K. R. Rajagopal and A. R. Srinivasa, On the thermomechanics of materials that have multiple natural configurations - part II: Twinning and solid to solid phase transformation,, Zeitschrift für Angewandte Mathematik und Physik, 55 (2004), 1074.
|
[31] |
K. R. Rajagopal and A. R. Srinivasa, On the response of non-dissipative solids,, Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci., 463 (2007), 357.
|
[32] |
K. R. Rajagopal and A. R. Srinivasa, On a class of non-dissipative materials that are not hyperelastic,, Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci., 465 (2009), 495.
|
[33] |
K. R. Rajagopal and A. R. Srinivasa, A Gibbs-potential-based formulation for obtaining the response functions for a class of viscoelastic materials,, Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci., 467 (2011), 39.
|
[34] |
K. R. Rajagopal and A. R. Srinivasa, "Restrictions Placed on Constitutive Relations by Angular Momentum Balance and Galilean Invariance,", In Press, (2012). Google Scholar |
[35] |
K. R. Rajagopal and A. S. Wineman, "Mechanical Response of Polymers,", Cambridge University Press, (2001). Google Scholar |
[36] |
I. J. Rao and K. R. Rajagopal, A thermodynamic framework for the study of crystallization in polymers,, Zeitschrift für Angewandte Mathematik und Physik, 53 (2002), 365.
|
[37] |
C. Truesdell, Mechanical Foundations of Elasticity and Fluid Dynamics,, Mechanics I, (1966), 125. Google Scholar |
[38] |
C. Truesdell and W. Noll, "Non-Linear Field Theories of Mechanics,", 2nd edition, (1992).
|
[1] |
Xin Zhong. Singularity formation to the nonhomogeneous magneto-micropolar fluid equations. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021021 |
[2] |
Zsolt Saffer, Miklós Telek, Gábor Horváth. Analysis of Markov-modulated fluid polling systems with gated discipline. Journal of Industrial & Management Optimization, 2021, 17 (2) : 575-599. doi: 10.3934/jimo.2019124 |
[3] |
Xiuli Xu, Xueke Pu. Optimal convergence rates of the magnetohydrodynamic model for quantum plasmas with potential force. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 987-1010. doi: 10.3934/dcdsb.2020150 |
[4] |
Lingyu Li, Jianfu Yang, Jinge Yang. Solutions to Chern-Simons-Schrödinger systems with external potential. Discrete & Continuous Dynamical Systems - S, 2021 doi: 10.3934/dcdss.2021008 |
[5] |
Yue-Jun Peng, Shu Wang. Asymptotic expansions in two-fluid compressible Euler-Maxwell equations with small parameters. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 415-433. doi: 10.3934/dcds.2009.23.415 |
[6] |
Wenlong Sun, Jiaqi Cheng, Xiaoying Han. Random attractors for 2D stochastic micropolar fluid flows on unbounded domains. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 693-716. doi: 10.3934/dcdsb.2020189 |
[7] |
Andrea Giorgini, Roger Temam, Xuan-Truong Vu. The Navier-Stokes-Cahn-Hilliard equations for mildly compressible binary fluid mixtures. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 337-366. doi: 10.3934/dcdsb.2020141 |
[8] |
Pavel Eichler, Radek Fučík, Robert Straka. Computational study of immersed boundary - lattice Boltzmann method for fluid-structure interaction. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 819-833. doi: 10.3934/dcdss.2020349 |
[9] |
Kengo Nakai, Yoshitaka Saiki. Machine-learning construction of a model for a macroscopic fluid variable using the delay-coordinate of a scalar observable. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1079-1092. doi: 10.3934/dcdss.2020352 |
[10] |
Noriyoshi Fukaya. Uniqueness and nondegeneracy of ground states for nonlinear Schrödinger equations with attractive inverse-power potential. Communications on Pure & Applied Analysis, 2021, 20 (1) : 121-143. doi: 10.3934/cpaa.2020260 |
[11] |
Pierluigi Colli, Gianni Gilardi, Gabriela Marinoschi. Solvability and sliding mode control for the viscous Cahn–Hilliard system with a possibly singular potential. Mathematical Control & Related Fields, 2020 doi: 10.3934/mcrf.2020051 |
[12] |
Gui-Qiang Chen, Beixiang Fang. Stability of transonic shock-fronts in three-dimensional conical steady potential flow past a perturbed cone. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 85-114. doi: 10.3934/dcds.2009.23.85 |
[13] |
Kai Yang. Scattering of the focusing energy-critical NLS with inverse square potential in the radial case. Communications on Pure & Applied Analysis, 2021, 20 (1) : 77-99. doi: 10.3934/cpaa.2020258 |
[14] |
Dan Zhu, Rosemary A. Renaut, Hongwei Li, Tianyou Liu. Fast non-convex low-rank matrix decomposition for separation of potential field data using minimal memory. Inverse Problems & Imaging, 2021, 15 (1) : 159-183. doi: 10.3934/ipi.2020076 |
[15] |
Tomáš Oberhuber, Tomáš Dytrych, Kristina D. Launey, Daniel Langr, Jerry P. Draayer. Transformation of a Nucleon-Nucleon potential operator into its SU(3) tensor form using GPUs. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1111-1122. doi: 10.3934/dcdss.2020383 |
[16] |
Yi-Ming Tai, Zhengyang Zhang. Relaxation oscillations in a spruce-budworm interaction model with Holling's type II functional response. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021027 |
[17] |
Javier Fernández, Cora Tori, Marcela Zuccalli. Lagrangian reduction of nonholonomic discrete mechanical systems by stages. Journal of Geometric Mechanics, 2020, 12 (4) : 607-639. doi: 10.3934/jgm.2020029 |
[18] |
Xuefei He, Kun Wang, Liwei Xu. Efficient finite difference methods for the nonlinear Helmholtz equation in Kerr medium. Electronic Research Archive, 2020, 28 (4) : 1503-1528. doi: 10.3934/era.2020079 |
[19] |
Riccarda Rossi, Ulisse Stefanelli, Marita Thomas. Rate-independent evolution of sets. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 89-119. doi: 10.3934/dcdss.2020304 |
[20] |
Dominique Chapelle, Philippe Moireau, Patrick Le Tallec. Robust filtering for joint state-parameter estimation in distributed mechanical systems. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 65-84. doi: 10.3934/dcds.2009.23.65 |
2019 Impact Factor: 1.233
Tools
Metrics
Other articles
by authors
[Back to Top]