Abstract
I consider the prescription of symmetry restrictions for constitutive functions in the continuum mechanics of solid crystals. The issues are well understood in the straightforward case which refers to homogeneous elastic deformation of a perfect single crystal, where the accepted procedure is to extrapolate the symmetries of a discrete set of atoms to the symmetries of the continuum, using the Cauchy-Born hypothesis. Ericksen [4] and Parry [11] discuss these issues in some detail.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
B.A. Bilby, Continuous distributions of dislocations. Progress in solid mechanics, (ed. I. Sneddon), vol.l. Amsterdam; North-Holland, 1960.
C. Davini, A proposal for a continuum theory of defective crystals, Arch. Rational Mech. Anal. 96 (1986) 295 - 317.
C. Davini and G.P. Parry, A complete list of invariants for defective crystals. Proc. R. Soc. Land. A. 432 (1991) 341 - 365.
J.L. Ericksen; Nonlinear elasticity of diatomic crystals, Int. J. Solids Structures 6 (1970) 951 - 958.
I. Fonseca and G.P. Parry, Equilibrium configurations of defective crystals, Arch. Rat. Mech. Anal. 120 (1992) 245 - 283.
K. Kondo, Non-Riemannian geometry of imperfect crystals from a macroscopic viewpoint, RAAG memoirs of the unifying study of basic problems in engineering and physical science by means of geometry (ed. K. Kondo), vol. 1. Tokyo: Gakuyusty Bunken Fukin-Day, 1955.
E. Kröner, Allgemeine Kontinuumstheorie der Versetzungen and Eigenspannungen, Arch. Rat. Mech. Anal. 4 (1960) 273 - 334.
E. Kröner, Continuum theory of defects, Physics of defects (ed. R. Ballian, M. Kléman and J.-P. Poirer), Amsterdam: North-Holland, 1981.
N.D. Mermin, D.S. Rokhsar and D.C. Wright, Beware of 46-Fold Symmetry: The Classification of Two-Dimensional Quasicrystallographic Lattices, Phys. Rev. Lett. 58 (1987) 2099 - 2101.
P. Olver, Invariants, Equivalence and Symmetry, (draft copy of) L.M.S. Lecture Notes, 1992.
G.P. Parry, On phase transitions involving internal strain, Int. J. Solids Structures 17 (1981) 361 - 378.
G.P. Parry, Defects and rearrangements in crystals, in Applied Mechanics Division, 148, ed. L.M. Brock, American Society of Mechanical Engineers, New York, 1992.
G.P. Parry, Elastic-plastic decompositions of defect-preserving changes of state in solid crystals, to appear in the proceedings of STAMM 94, Lisbon, 1994.
L.S. Pontryagin, Topological Groups (2nd edn.) Gordon and Breach, New York, London, Paris, 1955.
D.H. Sattinger, and O.L. Weaver, Lie groups and algebras with applications to physics, geometry and mechanics. Applied Mathematical Sciences 61, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 1986.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Parry, G.P. (1995). Material Symmetry in Solid Crystals. In: Parker, D.F., England, A.H. (eds) IUTAM Symposium on Anisotropy, Inhomogeneity and Nonlinearity in Solid Mechanics. Solid Mechanics and Its Applications, vol 39. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8494-4_31
Download citation
DOI: https://doi.org/10.1007/978-94-015-8494-4_31
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4589-8
Online ISBN: 978-94-015-8494-4
eBook Packages: Springer Book Archive