×

zbMATH — the first resource for mathematics

On the residual stress possible in an elastic body with material symmetry. (English) Zbl 0571.73011
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
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] B. D.Coleman & W.Noll, Material symmetry and thermostatic inequalities in finite elastic deformations.Arch. Rational Mech. Anal. 15 (1964) 87-111. · Zbl 0123.40703 · doi:10.1007/BF00249520
[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 · doi:10.1098/rspa.1962.0043
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.