The wavefront induced in a homogeneously shearing solid by a localized material imperfection
Author:
M. Toulios
Journal:
Quart. Appl. Math. 43 (1985), 225-235
MSC:
Primary 73D35
DOI:
https://doi.org/10.1090/qam/793531
MathSciNet review:
793531
Full-text PDF Free Access
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Abstract: The shape of the two dimensional wavefront induced by a line material imperfection in a large body which is being subjected to a homogeneous, time dependent antiplane shear deformation, is investigated. The body is composed of isotropic, incompressible, hyperelastic material and the constitutive relation is assumed to be such that depending on the value of one parameter, strong ellipticity fails at a strain level corresponding to the local maximum of the shear stress-strain curve. The wavefront shapes are compared when this occurs and when it does not.
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F. H. Wu and L. B. Freund, Deformation trapping due to thermoplastic instability in one-dimensional wave propagation, J. Mech. Phys. Solids 32, 119–132 (1984)
F. H. Wu, M. Toulios and L. B. Freund, Initiation and propagation of shear bands in antiplane shear deformation, Brown University Technical Report, March 1984
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R. Abeyaratne and N. Triantafyllidis, The emergence of shear bands in plane strain, Int. J. Solids Structures 17 1113–1134 (1981)
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J. K. Knowles, On finite antiplane shear for incompressible elastic materials, J. Austral. Math. Soc. Ser. B, 19, 400–415 (1976)
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D. C. Erlich, D. R. Curran and L. Seaman, Further developments of a computational shear band model, SRI Rept. AMMRC TR 80-3 (1980)
F. H. Wu and L. B. Freund, Deformation trapping due to thermoplastic instability in one-dimensional wave propagation, J. Mech. Phys. Solids 32, 119–132 (1984)
F. H. Wu, M. Toulios and L. B. Freund, Initiation and propagation of shear bands in antiplane shear deformation, Brown University Technical Report, March 1984
J. K. Knowles, The finite antiplane shear field near the tip of a crack for a class of incompressible elastic solids, Intl. J. of Fracture 13, 611–639 (1977)
L. Zee and E. Sternberg, Ordinary and strong ellipticity in the equilibrium theory of incompressible hyperelastic solids, Arch. Rational Mech. Anal. 83, 53–90 (1983)
R. Abeyaratne and N. Triantafyllidis, The emergence of shear bands in plane strain, Int. J. Solids Structures 17 1113–1134 (1981)
R. G. Payton, Two dimensional wavefront shape induced in a homogeneously strained elastic body by a point perturbing body force, Arch. Rational Mech. Anal. 32, 311–330 (1969)
J. K. Knowles, On finite antiplane shear for incompressible elastic materials, J. Austral. Math. Soc. Ser. B, 19, 400–415 (1976)
A. E. Green, R. S. Rivlin and R. T. Shield, General theory of small elastic deformations superposed on finite elastic deformations, Royal Society of London, Proceedings Ser. A., 211, 128–154 (1952)
A. C. Eringen and E. S. Suhubi, Elastodynamics, Vol. I, Academic Press, New York, 1974
R. Courant and D. Hilbert, Methods of mathematical physics, Vol. II, Interscience, New York, 1962
A. Jeffrey, Quasilinear hyperbolic systems and waves, Pitman Publishing, London, 1977
G. B. Whitham, Linear and nonlinear waves, John Wiley & Sons, New York, 1974
M. Hayes and R. S. Rivlin, Propagation of a plane wave in an isotropic elastic material subjected to pure homogeneous deformation, Arch. Rational Mech. Anal. 8, 15–22 (1961)
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Article copyright:
© Copyright 1985
American Mathematical Society
