Abstract
Well known results on the propagation and growth of acceleration waves in Cauchy elastic materials are extended to materials which suffer one or two internal constraints. It is proved, under certain restrictions, that acceleration waves will not propagate in a material which has three or more internal constraints. The great simplifications deriving from an assumption of hyperelasticity are indicated. The present results could be extended to materials other than simple elastic.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Wright, T.W., Arch. Rational Mech. Anal., 50, 237–277 (1973).
Truesdell, C., & W. Noll, Encyclopedia of Physics III/3. Ed. S. Flügge. Berlin Heidelberg New York: Springer 1965.
Chadwick, P., & P.K. Currie, Arch. Rational Mech. Anal., 49, 137–158 (1972).
Varley, E., Arch. Rational Mech. Anal., 19, 215–225 (1965).
Varley, E., & E. Cumberbatch, J. Inst. Maths. Applics., 1, 101–112 (1965).
Varley, E., & J. Dunwoody, J. Mech. Phys. Solids, 13, 17–28 (1965).
Chen, P.J., Arch. Rational Mech. Anal., 31, 228–254 (1968).
Suhubi, E.S., Int. J. Engng. Sci., 8, 699–710 (1970).
Ericksen, J.L., J. Rational Mech. Anal., 2, 329–337 (1953).
Chen, P.J., & M.E. Gurtin, Int. J. Solids Structures, 10, 275–281 (1974).
Spencer, A.J.M., “Deformations of Fibre-reinforced Materials”, Oxford, 1972.
Spencer, A.J.M., J. Mech. Phys. Solids, 22, 147–159 (1974).
Thomas, T.Y., “Plastic Flow and Fracture in Solids”. New York-London: Academic Press 1961.
Courant, R., & D. Hilbert, “Methods of Mathematical Physics”, Vol. II, Holden-Day, 1965.
Author information
Authors and Affiliations
Additional information
Communicated by J.L. Ericksen
Rights and permissions
About this article
Cite this article
Scott, N. Acceleration waves in constrained elastic materials. Arch. Rational Mech. Anal. 58, 57–75 (1975). https://doi.org/10.1007/BF00280154
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00280154