Free Access
Issue |
ESAIM: COCV
Volume 14, Number 1, January-March 2008
|
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Page(s) | 148 - 159 | |
DOI | https://doi.org/10.1051/cocv:2007050 | |
Published online | 21 September 2007 |
- S. Aubry and M. Ortiz, The mechanics of deformation-induced subgrain-dislocation structures in metallic crystals at large strains. Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 459 (2003) 3131–3158. [Google Scholar]
- B.A. Bilby, R. Bullough and E. Smith, Continuous distributions of dislocations: a new application of the methods of non-riemannian geometry. Proc. Roy. Soc. London, Ser. A 231 (1955) 263–273. [Google Scholar]
- E. Cartan, Leçons sur la géometrie des espaces de Riemann. Gauthier-Villars, Paris (1928). [Google Scholar]
- P. Cermelli and M.E. Gurtin, On the characterization of geometrically necessary dislocations in finite plasticity. J. Mech. Phys. Solids 49 (2001) 1539–1568. [CrossRef] [Google Scholar]
- S. Conti and M. Ortiz, Dislocation microstructures and the effective behavior of single crystals. Arch. Rat. Mech. Anal. 176 (2005) 103–147. [Google Scholar]
- A. Einstein, Relativity: The Special and General Theory. Crown, New-York (1961). [Google Scholar]
- J.D. Eshelby, The continuum theory of lattice defects, volume III of Solid state Physics. Academic Press, New-York (1956). [Google Scholar]
- G. Friesecke, R.D. James and S. Müller, A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity. Comm. Pure Appl. Math. 55 (2002) 1461–1506. [Google Scholar]
- M.E. Gurtin, An Introduction to Continuum Mechanics, Mathematics in Science and Engineering 158. Academic Press, London, 1st edn. (1981). [Google Scholar]
- M.E. Gurtin, On the plasticity of single crystals: free energy, microforces, plastic-strain gradients. J. Mech. Phys. Solids 48 (2000) 989–1036. [CrossRef] [MathSciNet] [Google Scholar]
- J.P. Hirth and J. Lothe, Theory of Dislocations. McGraw-Hill, New-York (1968). [Google Scholar]
- F. John, Rotation and strain. Comm. Pure Appl. Math. 14 (1961) 391–413. [CrossRef] [MathSciNet] [Google Scholar]
- J. Jost, Riemannian Geometry. Springer-Verlag (2002). [Google Scholar]
- K. Kondo, Geometry of elastic deformation and incompatibility, in Memoirs of the Unifying Study of the Basic Problems in Engineering Science by Means of Geometry, volume 1, Division C, K. Kondo Ed., Gakujutsu Bunken Fukyo-Kai (1955) 361–373. [Google Scholar]
- E. Kröner, Der fundamentale Zusammenhang zwischen Versetzungsdichte und Spannungsfunktion. Z. Phys. 142 (1955) 463–475. [Google Scholar]
- E. Kröner, Kontinuumstheorie der Versetzungen und Eigenspannungen, Ergebnisse der Angewandten Mathematik 5. Springer, Berlin (1958). [Google Scholar]
- E. Kröner, Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen. Arch. Rat. Mech. Anal. 4 (1960) 273–334. [Google Scholar]
- E. Kröner and A. Seeger, Nichtlineare Elastizitätstheorie der Versetzungen und Eigenspannungen. Arch. Rat. Mech. Anal. 3 (1959) 97–119. [CrossRef] [Google Scholar]
- D. Kuhlmann-Wilsdorf, Theory of plastic deformation: properties of low energy dislocation structures. Mat. Sci. Eng. A113 (1989) 1. [Google Scholar]
- E.H. Lee, Elastic-plastic deformation at finite strain. J. Appl. Mech. 36 (1969) 1–6. [Google Scholar]
- A. Mielke and S. Müller, Lower semi-continuity and existence of minimizers in incremental finite-strain elastoplasticity. ZAMM 86 (2006) 233–250. [Google Scholar]
- T. Mura, Micromechanics of defects in solids. Kluwer Academic Publishers, Boston (1987). [Google Scholar]
- F.R.N. Nabarro, Theory of crystal dislocations. Oxford University Press, Oxford (1967). [Google Scholar]
- J. Necas and I. Hlavacek, Mathematical theory of elastic and elastico-plastic bodies: An introduction. Elsevier, Amsterdam (1981). [Google Scholar]
- P. Neff, On Korn's first inequality with nonconstant coefficients. Proc. Roy. Soc. Edinb. A 132 (2002) 221–243. [CrossRef] [Google Scholar]
- J.F. Nye, Some geometrical relations in dislocated crystals. Acta Metall. 1 (1953) 153–162. [CrossRef] [Google Scholar]
- M. Ortiz and E.A. Repetto, Nonconvex energy minimization and dislocation structures in ductile single crystals. J. Mech. Phys. Solids 47 (1999) 397–462. [Google Scholar]
- M. Ortiz, E.A. Repetto and L. Stainier, A theory of subgrain dislocation structures. J. Mech. Phys. Solids 48 (2000) 2077–2114. [CrossRef] [MathSciNet] [Google Scholar]
- G.P. Parry and M. Silhavy, Elastic scalar invariants in the theory of defective crystals. R. Soc. Lond. Proc., Ser. A, Math. Phys. Eng. Sci. 455 (1999) 4333–4346. [Google Scholar]
- Yu.G. Reshetnyak, Liouville's theorem on conformal mappings for minimal regularity assumptions. Siberian Math. J. 8 (1967) 631–653. [Google Scholar]
- B. Svendsen, Continuum thermodynamic models for crystal plasticity including the effects of geometrically necessary dislocations. J. Mech. Phys. Solids 50 (2002) 1297–1329. [CrossRef] [MathSciNet] [Google Scholar]
- R.M. Wald, General Relativity. University of Chicago Press, Chicago (1984). [Google Scholar]
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