Thermodynamics, stability and non-linear oscillations of viscoelastic solids - I. Differential type solids of second grade

International Journal of Non-Linear Mechanics

Volumn 31, Issue 4, 1996, Pages 495-516

  Fosdick, Roger L ^a   Yu, Jang Horng ^a  

^a University of Minnesota   (United States)

Author keywords

Stability; Thermodynamics; Viscoelastic solids

Indexed keywords

CONTINUUM MECHANICS; FREE ENERGY; MICROSTRUCTURE; MODELS; NEWTONIAN FLOW; OSCILLATIONS; SOLIDS; STABILITY; THERMODYNAMICS; VISCOSITY;

CENTER OF MASS; FREE OSCILLATION; LOCAL MINIMUM IN EQUILIBRIUM; MICROSTRUCTURAL COEFFICIENTS; NEWTONIAN VISCOSITY; NON LINEAR OSCILLATIONS; SECOND GRADE SOLIDS; STABILITY THEOREM; THERMODYNAMIC COMPATIBILITY; VISCOELASTIC SOLIDS;

VISCOELASTICITY;

EID: 0030196354     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/0020-7462(96)00005-4     Document Type: Article

References (13)

1. C. Truesdell and W. Noll, The non-linear field theories of mechanics. Handbook of Physics, Vol. III/3. Springer, New York (1965).
2. R. L. Fosdick and J.-H. Yu, Thermodynamics, stability and nonlinear oscillations of viscoelastic solids, Part II: History type solids. Int. J. Non-Linear Mechanics (to appear).
3. R. S. Rivlin and J. L. Eriksen, Stress-deformation relations for isotropic materials. J. Rational Mech. Anal. 4, 323 (1955).
4. R. L. Fosdick, W. H. Warner and J.-H. Yu, Steady, structured shock wave in a viscoelastic solid of differential type. Int. J. Engng Sci. 28, 469 (1990).
5. R. L. Fosdick, Y, Ketema and J.-H. Yu, Dynamics of a viscoelastic spherical shell with a nonconvex strain energy function. Quart. Appl. Math. (to appear).
6. J. E. Dunn and R. L. Fosdick, Thermodynamics, stability and boundness of fluids of complexity 2 and fluids of second grade. Archive Rational Mech. Anal. 56, 191 (1974).
7. J.-H. Yu, Nonlinear oscillations of viscoelastic cylindrical and spherical shells. Ph.D. thesis, University of Minnesota (1994).
8. L. E. Payne and H. F. Weinberger, An optimal Poincaré inequality for convex domains. Archive Rational Mech. Anal. 5, 286 (1960).
9. L. E. Payne and H. F. Weinberger, On Korn's inequality. Archive Rational Mech. Anal. 8, 89 (1961).
10. R. Walter, Principles of Mathematical Analysis, 3rd Edition. McGraw Hill, New York (1976).
11. J. K. Knowles, Large amplitude oscillations of a tube of incompressible elastic material. Quart. Appl. Math. 18, 71 (1960).
12. M. Baker and J. L. Ericksen, Inequalities restricting the form of the stress-deformation relations for isotropic elastic solids and Reiner-Rivlin fluids. J. Wash. Acad. Sci. 44, 33 (1954).
13. R. L. Fosdick and G. P. MacSithigh, Minimization in incompressible nonlinear elastic theory. J. Elasticity 16, 267 (1986).