Summary
A homogeneous deformation field, called “pure extension” is introduced. Various applications of this field are considered. Pure extension leads to a reasonable static interpretation of the strong-ellipticity condition in linearised elasticity theory. The response of a compressible elastic material to pure extension is related to the speeds of propagation of infinitesimal plane waves. Finally, a generalised Tension-Extension condition is introduced and discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ericksen, J.L., Deformations possible in every compressible, isotropic, perfectly-elastic material. J. Math. Phys. 34, 126–128 (1955).
Truesdell, C., & R. Toupin, Static grounds for inequalities in finite strain of elastic materials. Arch. Rational Mech. Anal. 12, 1–33 (1963).
Truesdell, C., & W. Noll, The Non-linear Field Theories of Mechanics. Flügge's Encyclopedia of Physics, III/3. Berlin-Heidelberg-New York: Springer 1965.
Morrey, C.B., Jr., Second order elliptic systems of differential equations, Contrib. Theory Partial Diff. Eqns., Annals Math. Studies No. 33, 101–159 (1954).
Zorski, H., On the Equations Describing Small Deformations Superimposed on Finite Deformations. Proc. Int. Sympos. Second Order Effects, Ed. by M. Reiner & D. Abir, pp. 109–128. London: Pergamon 1964.
Hayes, M., Uniqueness for the mixed boundary-value problem in the theory of small deformations superimposed on large. Arch. Rational Mech. Anal. 16, 238–242 (1964).
Gurtin, M. E., & R. A. Toupin, A uniqueness theorem for the displacement boundaryvalue problem of linear elastodynamics. Q. Appl. Math. 23, 79–81 (1965).
Toupin, R. A., & B. Bernstein, Sound waves in deformed perfectly elastic materials. Acoustoelastic effect. J. Acoust. Soc. Amer. 33, 216–225 (1961).
Hill, R., Acceleration waves in solids. J. Mech. Phys. Solids 10, 1–16 (1962).
Shield, R. T., On the stability of linear continuous systems. ZAMP 16, 649–686 (1965).
Knops, R. J., & E. W. Wilkes, On Mochvan's theorems for stability of continuous systems. Int. J. Eng. Sci. 4, 303–329 (1966).
Kirchhoff, G., Über die Gleichungen des Gleichgewichts eines elastischen Körpers bei nicht unendlich kleinen Verschiebungen seiner Theile. Akad. Wiss. Wien 9, 762–773 (1852).
Author information
Authors and Affiliations
Additional information
Communicated by C. Truesdell
Rights and permissions
About this article
Cite this article
Hayes, M. On pure extension. Arch. Rational Mech. Anal. 28, 155–164 (1968). https://doi.org/10.1007/BF00283863
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00283863