Despite the technological relevance of anisotropic nonlinear viscoelastic solids, little effort has been expended in the development of specific constitutive theories. In this study we develop a constitutive model for describing the nonlinear response of anisotropic viscoelastic solids that might be well suited to describe the response of biological and geological solids. The model is an integral model that takes into account the history of deformation of the body. Using the model a few boundary value problems are studied, namely the time dependent extension and shearing of such bodies.
Pipkin, A.C. and Rogers, T.G.A non-linear integral representation for viscoelastic behaviour. Journal of Mechanics and Physics of Solids, 16, 59-72 (1968).
2.
Wineman, A.S.Large axisymmetric stretching of a non-linear viscoelastic membrane due to spinning, Journal of Applied Mechanics, 39, 946-952 (1972).
3.
Thomson, W. (Lord Kelvin), On the elasticity and viscosity of metals. Proceedings of the Royal Society of London A14, 289-297 (1965).
4.
Voigt, W.Ueber innere Reibung fester Korper, insbesondere der Metalle, Annalen der Physik, 283, 671-693 (1892).
5.
Rajagopal, K.R. and Saccomandi, G.Shear waves in a class of non-linear viscoelastic solids, Quarterly Journal of Mechanics and Applied Mathematics , 56, 311-326 (2003).
6.
Wineman, A.S. and Rajagopal, K.R.Mechanical Response of Polymers, An Introduction, Cambridge University Press, Cambridge, 2000 .
7.
Johnson, G.A. , Livesay, G.A., Woo, S.L.Y. and Rajagopal , K.R.A single integral finite strain (SIFS) viscoelastic model of ligaments and tendons, Advances in Bioengineering, 22, 245-248 (1992).
8.
Bowen, R.M.Mechanics of Mixtures, in Continuum Physics, Vol. III, ed. A. C. Eringen, Academic, New York, 1976.
9.
Atkin, R.J. and Craine, R.E.Continuum theories of mixtures: applications. Journal of the Institute of Mathematics and Applications, 17, 153-207 (1976).
Samohyl, I.Thermodynamics of Irreversible Processes in Fluid Mixtures, Teubner, Leipzig, 1987.
12.
Rajagopal, K.R. and Tao, L.Mechanics of Mixtures, World Scientific, Singapore, 1995 .
13.
Rajagopal, K.R., Gandhi, M.V. and Wineman, A.S.On boundary conditions for a certain class of problems in mixture theory. International Journal of Engineering Science, 24, 1453-1463 (1986).
14.
Prasad, S.C. and Rajagopal, K.R.On the diffusion of fluids through solids undergoing large deformations. Mathematics and Mechanics of Solids, 11, 91-105 (2006).
15.
Spencer, A.J.M.Theory of Invariants, in Continuum Physics, Vol. I, pp. 259-353, ed. A. C. Eringen, Academic, New York, 1971.
16.
Fung, Y.C.Biomechanics: Mechanical Properties of Living Tissues, Springer, New York, 1981.
17.
Linz, P.Analytical and Numerical Methods for Volterra Equations, SIAM Studies in Applied Mathematics, SIAM, Philadelphia , 1985.
18.
Wineman, A.S.Universal deformations of incompressible simple materials. University of Michigan Technical Report, Ann Arbor, 1967.
19.
Carroll, M.M.Controllable deformations of incompressible simple materials. International Journal of Engineering Science , 5, 515-525, (1967).
20.
Fosdick, R.L.Dynamically possible motions of incompressible, isotropic, simple materials. Archive for Rational Mechanics and Analysis, 29, 272-288 (1968).
