On the residual stress possible in an elastic body with material symmetry. (English) Zbl 0571.73011

Hoger, Anne

Arch. Ration. Mech. Anal. 88, 271-289 (1985).

Residual stress possible in a body depends on the shape of the body and the boundary conditions. Thus a nonzero residual stress must be nonuniform. The author examines the dependence of residual stress on material symmetry and concludes, among other general results, that: an isotropic body can support no residual stress; and a transversely isotropic body with a uniform axis of symmetry can support no residual stress.
This is a clearly written paper in a rigorous mathematical style characteristic of the journal where it appears. Of interest to specialists in the field.

Reviewer: R.H.Lance

MSC:

74B99	Elastic materials
74B20	Nonlinear elasticity
74E10	Anisotropy in solid mechanics
74E15	Crystalline structure

Keywords:

shape; boundary conditions; nonzero residual stress; nonuniform; material symmetry; isotropic body; no residual stress; transversely isotropic body; uniform axis of symmetry

References:

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[2]	M. E.Gurtin,An Introduction to Continuum Mechanics. Academic Press, New York (1981). · Zbl 0559.73001
[3]	M. E.Gurtin, The linear theory of elasticity.Handbuch der Physik VIa/2, Springer-Verlag, Berlin Heidelberg New York (1972). · Zbl 0317.73002
[4]	A. E.Green, Thermoelastic stresses in initially stressed bodies.Proc. Roy. Soc., A 266 (1962) 1-19. · Zbl 0111.37503