Keywords:
- Analytical solutions
- Blood vessel
- Burgers fluid
- Cauchy stress
- Colombeau algebra
- constitutive modelling
- constitutive relations
- Convected coordinates
- Couette flow
- Cylindrical Couette flow
- Deviatoric strain
- Dirichlet and Neumann boundary conditions
- Elasticity
- electrorheological fluids
- Euler--Bernoulli beam theory
- Exact solution
- existence
- existence result for large data
- experimental error
- falling cylinder viscometer
- Generalized Navier-Stokes-Fourier system
- Gibbs free energy
- Gibbs potential
- Granular materials
- Hagen–Poiseuille flow
- Heat flux
- Helmholtz potential
- Hencky strain
- implicit constitutive relations
- Implicit constitutive theory
- Incompressible fluid
- Incompressible fluids
- Internal energy
- jump coditions
- jump discontinuities
- Kelvin-Voigt model
- large data existence
- Large deformation
- Maximization and rate of entropy production
- Maxwell fluid
- mean normal stress
- Mixture
- Navier-Stokes fluid
- Navier-Stokes-Fourier system
- Navier’s slip boundary condition
- Navier’s slip boundary conditions
- non-linear wave equation
- nonlinear elasticity
- numerical simulation
- Oberbeck--Boussinesq approximation
- ordinary differential equations
- Poiseuille flow
- Power-law fluids
- pressure
- pressure dependent material moduli
- pressure dependent viscosity
- Pressure-dependent viscosity
- Rate of dissipation
- Rate type fluid
- regularity
- Rheology
- second grade fluid
- shear rate dependent viscosity
- shear-dependent viscosity
- small strain
- spatially periodic problem
- spectral collocation method
- stability
- Stokes’ second problem
- stress dependent material moduli
- Stress power
- Stress power-law fluids
- suitable weak solution
- temperature-dependent viscosity
- thermal expansivity
- thermodynamic pressure
- thermodynamics
- uniqueness
- unsteady flows
- viscoelastic fluids
- viscoelastic materials
- viscoelastic solid
- weak solution
Publications of Rajagopal, K. R.
2021
| and , Implicit type constitutive relations for elastic solids and their use in the development of mathematical models for viscoelastic fluids (2021), in: Fluids, 6:3 |
[DOI] |
| , and , Unconditional finite amplitude stability of a fluid in a mechanically isolated vessel with spatially non-uniform wall temperature (2021), in: Continuum Mechanics and Thermodynamics, 33(515–543) |
[DOI] |
2020
| , and , Gibbs free energy based representation formula within the context of implicit constitutive relations for elastic solids (2020), in: International Journal of Non-Linear Mechanics, 121(103433) |
[DOI] |
2018
| and , A new class of models to describe the response of electrorheological and other field dependent fluids, in: Generalized models and non-classical approaches in complex materials 1, Springer, 2018 |
[DOI] |
| , and , Numerical simulations of an incompressible piezoviscous fluid flowing in a plane slider bearing (2018), in: Meccanica, 53:1-2(209--228) |
[DOI] |
2017
| , , , and , Determination of pressure data from velocity data with a view towards its application in cardiovascular mechanics. Part 2: a study of aortic valve stenosis. (2017), in: International Journal of Engineering Science |
|
2016
| , and , A thermodynamically compatible model for describing asphalt binders: solutions of problems (2016), in: International Journal of Pavement Engineering, 17:6(550-564) |
[DOI] |
| , , , and , Determination of pressure data from velocity data with a view toward its application in cardiovascular mechanics. Part 1. Theoretical considerations (2016), in: International Journal of Engineering Science, 105(108 - 127) |
[DOI] [URL] |
| , and , Euler–Bernoulli type beam theory for elastic bodies with nonlinear response in the small strain range (2016), in: Archives of Mechanics, 68:1(3-25) |
[URL] |
| , and , On power-law fluids with the power-law index proportional to the pressure (2016), in: Applied Mathematics Letters, 62(118--123) |
[DOI] |
| and , On the response of physical systems governed by non-linear ordinary differential equations to step input (2016), in: International Journal of Non-Linear Mechanics, 81(207–221) |
[DOI] |
| , and , Response of a class of mechanical oscillators described by a novel system of differential-algebraic equations (2016), in: Applications of Mathematics, 61:1(79--102) |
[DOI] |
2015
| , and , A thermodynamically compatible model for describing the response of asphalt binders (2015), in: International Journal of Pavement Engineering, 16:4(297-314) |
[DOI] |
| , , and , Existence of solutions for the anti-plane stress for a new class of "strain-limiting" elastic bodies (2015), in: Calculus of Variations and PDE's, 54:2(2115--2147) |
[DOI] |
| , Modelling the flow of traffic, 2015 |
[URL] |
| , and , On a variant of the Maxwell and Oldroyd-B models within the context of a thermodynamic basis (2015), in: International Journal of Non-Linear Mechanics, 76(42--47) |
[DOI] |
| , , and , Vibrations of a lumped parameter mass-spring-dashpot system wherein the spring is described by a non-invertible elongation-force constitutive function (2015), in: International Journal of Non-Linear Mechanics, 76(154–163) |
[DOI] |
2014
| , and , Flow of a Burgers fluid due to time varying loads on deforming boundaries (2014), in: Journal of Non-Newtonian Fluid Mechanics, 210(66--77) |
[DOI] |
| , , and , On elastic solids with limiting small strain: modelling and analysis (2014), in: EMS Surveys in Mathematical Sciences, 1:2(283–332) |
[DOI] |
| , On implicit constitutive theories, 2014 |
[URL] |
| , , and , On the natural structure of thermodynamic potentials and fluxes in the theory of chemically non-reacting binary mixtures (2014), in: Acta Mechanica, 225:11(3157-3186) |
[DOI] |
2013
| and , A note on the modeling of incompressible fluids with material moduli dependent on the mean normal stress (2013), in: International Journal of Non-Linear Mechanics, 52:41-45 |
[DOI] |
| , and , Fidelity of the estimation of the deformation gradient from data deduced from the motion of markers placed on a body that is subject to an inhomogeneous deformation field (2013), in: Journal of Biomechanical Engineering, 135:8 |
[DOI] |
| and , On models for viscoelastic materials that are mechanically incompressible and thermally compressible or expansible and their Oberbeck–Boussinesq type approximations (2013), in: Mathematical Models and Methods in Applied Sciences, 23:10(1761--1794) |
[DOI] |
| , Particle free bodies, 2013 |
|
2012
| , , , and , A Thermodynamically Compatible Rate Type Fluid to Describe the Response of Asphalt (2012), in: Mathematics and Computers in Simulation, 82:10(1853--1873) |
[DOI] [URL] |
| and , Flow of an electrorheological fluid between eccentric rotating cylinders (2012), in: Theoretical and Computational Fluid Dynamics, 26:1-4(1-21) |
[DOI] |
| , , , and , On flows of fluids described by an implicit constitutive equation characterized by a maximal monotone graph, in: Mathematical Aspects of Fluid Mechanics, pages 23--51, Cambridge University Press, 2012 |
[URL] |
| and , On implicit constitutive relations for materials with fading memory (2012), in: Journal of Non-Newtonian Fluid Mechanics, 181–182(22-29) |
[DOI] [URL] |
| , and , On Kelvin-Voigt model and its generalizations (2012), in: Evolution Equations and Control Theory, 1:1(17-42) |
[DOI] [URL] |
| , and , On the Development and Generalizations of Allen-Cahn and Stefan Equations within a Thermodynamic Framework (2012), in: ZAMP - Zeitschrift für Angewandte Mathematik und Physik(1--18) |
[DOI] [URL] |
| , and , On the development and generalizations of Cahn-Hilliard equations within a thermodynamic framework (2012), in: ZAMP - Zeitschrift für Angewandte Mathematik und Physik, 63:1(145-169) |
[DOI] |
| , and , Role of pressure dependent viscosity in measurements with falling cylinder viscometer (2012), in: International Journal of Non-Linear Mechanics, 47:7(743–750) |
[DOI] |
2011
| and , A note on the decay of vortices in a viscous fluid (2011), in: Meccanica, 46:4(875-880) |
[DOI] [URL] |
| , , and , Further remarks on simple flows of fluids with pressure dependent viscosities (2011), in: Nonlinear Analysis: Real World Applications, 12:1(394-402) |
[DOI] [URL] |
| and , Jump Conditions in Stress Relaxation and Creep Experiments of Burgers Type Fluids-A Study in the Application of Colombeau Algebra of Generalized Functions (2011), in: ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 62:4(707–740) |
[DOI] [URL] |
| , and , On Maxwell fluid with relaxation time and viscosity depending on the pressure (2011), in: International Journal of Non-Linear Mechanics, 46:6(819-827) |
[DOI] [URL] |
| , and , On The Need For Compatibility Of Thermal And Mechanical Data In Flow Problems (2011), in: International Journal of Engineering Science, 49:7(537--543) |
[DOI] [URL] |
2010
| and , Compressible Generalized Newtonian Fluids (2010), in: ZAMP - Zeitschrift für Angewandte Mathematik und Physik, 61:6(1097-1110) |
[DOI] [URL] |
| , and , Generalizations of the Navier--Stokes fluid from a new perspective (2010), in: International Journal of Engineering Science, 48:12(1907-1924) |
[DOI] [URL] |
| , , and , On the Modelling of the Synovial Fluid (2010), in: Advances in Tribology, 2010(1--12) |
[DOI] [URL] |
| , and , Stress concentration due to an elliptic hole in a degrading linearized elastic solid (2010), in: International Journal of Applied Mechanics and Engineering, 15:1(35-49) |
2009
| , and , Analysis of the flows of incompressible fluids with pressure dependent viscosity fulfilling {$\nu(p,\cdot)\to+\infty$} as {$p\to+\infty$} (2009), in: Czechoslovak Math. J., 59(134):2(503--528) |
[DOI] [URL] |
| , and , Mathematical analysis of unsteady flows of fluids with pressure, shear-rate, and temperature dependent material moduli that slip at solid boundaries (2009), in: SIAM J. Math. Anal., 41:2(665--707) |
[DOI] [URL] |
| , and , Mathematical Results Concerning the Unsteady Flows of Chemically Reacting Incompressible Fluids, chapter 2, pages 26--53, Cambridge University Press, London Mathematical Society Lecture Note Series, volume 364, 2009 |
[URL] |
2008
| and , A thermodynamic framework for a mixture of two liquids (2008), in: Nonlinear Anal. Real World Appl., 9:4(1649--1660) |
[DOI] |
| , , and , Flows of incompressible fluids subject to Navier's slip on the boundary (2008), in: Computers & Mathematics with Applications, 56:8(2128--2143) |
[DOI] [URL] |
2007
| and , Incompressible rate type fluids with pressure and shear-rate dependent material moduli (2007), in: Nonlinear Anal. Real World Appl., 8:1(156--164) |
[DOI] |
| , and , Navier's slip and evolutionary Navier-Stokes-like systems with pressure and shear-rate dependent viscosity (2007), in: Indiana Univ. Math. J., 56:1(51--85) |
[DOI] |
2006
| and , Mathematical properties of the equations governing the flow of fluids with pressure and shear rate dependent viscosities, chapter 7, pages 407--444, Elsevier B. V., Handbook of Mathematical Fluid Dynamics, volume 4, 2006 |
[DOI] [URL] |
| and , On the modeling of inhomogeneous incompressible fluid-like bodies (2006), in: Mechanics of Materials, 38(233-242) |
[DOI] |