Initial stresses in elastic solids: Constitutive laws and acoustoelasticity

Wave Motion

Volumn 48, Issue 7, 2011, Pages 552-567

  Shams, M ^a,e   Destrade, M ^b,c   Ogden, R W ^a,c,d  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

^b NATIONAL UNIVERSITY OF IRELAND   (Ireland)

^c UNIVERSITY COLLEGE DUBLIN   (Ireland)

^d UNIVERSITY OF ABERDEEN   (United Kingdom)

^e NATIONAL UNIVERSITY OF SCIENCES AND TECHNOLOGY   (Pakistan)

Author keywords

Biot's theory; Initial stress; Invariants; Nonlinear elasticity; Plane waves; Residual stress

Indexed keywords

DEFORMATION; ELASTIC WAVES; EQUATIONS OF MOTION; INCOMPRESSIBLE FLOW; NONLINEAR EQUATIONS; RESIDUAL STRESSES; TENSORS; WAVE PROPAGATION;

BIOT'S THEORY; INITIAL STRESS; INVARIANTS; NONLINEAR ELASTICITY; PLANE WAVE;

ELASTICITY;

BIOT THEORY; DEFORMATION; ELASTICITY; ISOTROPY; NONLINEAR WAVE; RESIDUAL STRESS; WAVE EQUATION; WAVE PROPAGATION;

EID: 80052339798     PISSN: 01652125     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.wavemoti.2011.04.004     Document Type: Article

References (28)

1. Biot M.A. Non-linear theory of elasticity and the linearized case for a body under initial stress. Phil. Mag. 1939, 27:468-489.
2. Biot M.A. The influence of initial stress on elastic waves. J. Appl. Phys. 1940, 11:522-530.
3. Biot M.A. Mechanics of Incremental Deformations 1965, John Wiley, New York.
4. Boulanger P., Hayes M. Bivectors and Waves in Mechanics and Optics 1993, Chapman & Hall.
5. Chadwick P. The application of the Stroh formulation to prestressed elastic media. Math. Mech. Solids 1997, 2:379-403.
6. Chadwick P., Ogden R.W. On the definition of elastic moduli. Arch. Rat. Mech. Anal. 1971, 44:41-53.
7. Destrade M., Gilchrist M.D., Saccomandi G. Third- and fourth-order constants of incompressible soft solids and the acousto-elastic effect. J. Acoust. Soc. Am. 2010, 127:2759-2763.
8. Hayes M., Rivlin R.S. Propagation of a plane wave in an isotropic elastic material subjected to pure homogeneous deformation. Arch. Rat. Mech. Anal. 1961, 8:15-22.
9. Hoger A. On the residual stress possible in an elastic body with material symmetry. Arch. Rat. Mech. Anal. 1985, 88:271-290.
10. Hoger A. On the determination of residual stress in an elastic body. J. Elasticity 1986, 16:303-324.
11. Hoger A. The elasticity tensors of a residually stressed material. J. Elasticity 1993, 31:219-237.
12. Holzapfel G.A., Ogden R.W. Modelling the layer-specific 3D residual stresses in arteries, with an application to the human aorta. J. R. Soc. Interface 2010, 7:787-799.
13. Hughes D.S., Kelly J.L. Second-order elastic deformation of solids. Phys. Rev. 1953, 92:1145-1149.
14. Johnson B.E., Hoger A. The dependence of the elasticity tensor on residual stress. J. Elasticity 1993, 33:145-165.
15. Man C.-S. Hartig's law and linear elasticity with initial stress. Inv. Prob. 1998, 14:313-319.
16. Man C.-S., Lu W.Y. Towards an acoustoelastic theory for measurement of residual stress. J. Elasticity 1987, 17:159-182.
17. Murnaghan F.D. Finite deformations of an elastic solid. Am. J. Mathematics 1937, 59:235-260.
18. Ogden R.W. Non-Linear Elastic Deformations 1984, Ellis Horwood, Chichester.
19. Ogden R.W. Nonlinear elasticity, anisotropy and residual stresses in soft tissue. Biomechanics of Soft Tissue in Cardiovasular Systems 2003, 65-108. Springer, Wien. G.A. Holzapfel, R.W. Ogden (Eds.).
20. Ogden R.W. Incremental statics and dynamics of pre-stressed elastic materials. Waves in Nonlinear Pre-Stressed Materials 2007, 1-26. Springer, Wien. M. Destrade, G. Saccomandi (Eds.).
21. R.W. Ogden and B. Singh, Propagation of waves in an incompressible transversely isotropic elastic solid with initial stress: Biot revisited, J. Mech. Mat. Structures, to appear (2011).
22. Saravanan U. Representation for stress from a stressed reference configuration. Int. J. Eng. Sci. 2008, 46:1063-1076.
23. N.H. Scott, Some motions of fibre reinforced elastic materials, Ph.D. Thesis, University of East Anglia (1974).
24. Scott N.H., Hayes M. A note on wave propagation in internally constrained hyperelastic materials. Wave Motion 1985, 7:601-605.
25. Spencer A.J.M. Theory of invariants. Continuum Physics 1971, vol. 1:239-353. Academic Press, New York. A.C. Eringen (Ed.).
26. Toupin R.A., Bernstein B. Sound waves in deformed perfectly elastic materials. Acoustoelastic effect. J. Acoust. Soc. Am. 1961, 33:216-225.
27. Truesdell C. General and exact theory of waves in finite elastic strain. Arch. Rat. Mech. Anal. 1961, 8:263-296.
28. Zheng Q.-S. Theory of representations for tensor functions-a unified invariant approach to constitutive equations. Appl. Mech. Rev. 1994, 47:545-587.