Free Access
Issue
ESAIM: COCV
Volume 16, Number 2, April-June 2010
Page(s) 337 - 355
DOI https://doi.org/10.1051/cocv/2009002
Published online 10 February 2009
  1. E. Acerbi and N. Fusco, Semicontinuity problems in the calculus of variations. Arch. Rational Mech. Anal. 86 (1984) 125–145. [CrossRef] [MathSciNet]
  2. I. Aganović, J. Tambača and Z. Tutek, Derivation and justification of the models of rods and plates from linearized three-dimensional micropolar elasticity. J. Elasticity 84 (2006) 131–152. [CrossRef] [MathSciNet]
  3. J.M. Ball, Convexity conditions and existence theorems in nonlinear elasticity. Arch. Rational Mech. Anal. 63 (1976/1977) 337–403.
  4. P.G. Ciarlet, Mathematical elasticity, Volume I: Three-dimensional elasticity. North-Holland Publishing Co., Amsterdam (1988).
  5. E. Cosserat and F. Cosserat, Théorie des corps déformables. Librairie Scientifique A. Hermann et Fils (Translation: Theory of deformable bodies, NASA TT F-11 561, 1968), Paris (1909).
  6. B. Dacorogna, Direct methods in the calculus of variations. Second Edition, Springer (2008).
  7. A.C. Eringen, Microcontinuum Field Theories, Volume 1: Foundations and Solids. Springer-Verlag, New York (1999).
  8. I. Hlaváček and M. Hlaváček, On the existence and uniqueness of solution and some variational principles in linear theories of elasticity with couple-stresses. I. Cosserat continuum. Appl. Mat. 14 (1969) 387–410.
  9. J. Jeong and P. Neff, Existence, uniqueness and stability in linear Cosserat elasticity for weakest curvature conditions. Math. Mech. Solids (2008) DOI: 10.1177/1081286508093581.
  10. J. Jeong, H. Ramezani, I. Münch and P. Neff, Simulation of linear isotropic Cosserat elasticity with conformally invariant curvature. ZAMM Z. Angew. Math. Mech. (submitted).
  11. P.M. Mariano and G. Modica, Ground states in complex bodies. ESAIM: COCV (2008) DOI: 10.1051/cocv:2008036. [EDP Sciences]
  12. N.G. Meyers, Quasi-convexity and lower semi-continuity of multiple variational integrals of any order. Trans. Amer. Math. Soc. 119 (1965) 125–149. [CrossRef] [MathSciNet]
  13. P. Neff, On Korn's first inequality with nonconstant coefficients. Proc. R. Soc. Edinb. Sect. A 132 (2002) 221–243. [CrossRef]
  14. P. Neff, Existence of minimizers for a geometrically exact Cosserat solid. Proc. Appl. Math. Mech. 4 (2004) 548–549. [CrossRef]
  15. P. Neff, A geometrically exact Cosserat-shell model including size effects, avoiding degeneracy in the thin shell limit. Part I: Formal dimensional reduction for elastic plates and existence of minimizers for positive Cosserat couple modulus. Cont. Mech. Thermodynamics 16 (2004) 577–628. [CrossRef]
  16. P. Neff, The Cosserat couple modulus for continuous solids is zero viz the linearized Cauchy- stress tensor is symmetric. ZAMM Z. Angew. Math. Mech. 86 (2006) 892–912. [CrossRef] [MathSciNet]
  17. P. Neff, Existence of minimizers for a finite-strain micromorphic elastic solid. Proc. Roy. Soc. Edinb. A 136 (2006) 997–1012. [CrossRef]
  18. P. Neff, A finite-strain elastic-plastic Cosserat theory for polycrystals with grain rotations. Int. J. Eng. Sci. 44 (2006) 574–594. [CrossRef]
  19. P. Neff, A geometrically exact planar Cosserat shell-model with microstructure. Existence of minimizers for zero Cosserat couple modulus. Math. Meth. Appl. Sci. 17 (2007) 363–392. [CrossRef]
  20. P. Neff and K. Chelminski, A geometrically exact Cosserat shell-model for defective elastic crystals. Justification via Γ-convergence. Interfaces and Free Boundaries 9 (2007) 455–492. [CrossRef] [MathSciNet]
  21. P. Neff and S. Forest, A geometrically exact micromorphic model for elastic metallic foams accounting for affine microstructure. Modelling, existence of minimizers, identification of moduli and computational results. J. Elasticity 87 (2007) 239–276. [CrossRef] [MathSciNet]
  22. P. Neff and J. Jeong, A new paradigm: the linear isotropic Cosserat model with conformally invariant curvature. ZAMM Z. Angew. Math. Mech. (submitted).
  23. P. Neff and I. Münch, Curl bounds Grad on SO(3). ESAIM: COCV 14 (2008) 148–159. [CrossRef] [EDP Sciences]
  24. W. Pompe, Korn's first inequality with variable coefficients and its generalizations. Commentat. Math. Univ. Carolinae 44 (2003) 57–70.
  25. J. Tambača and I. Velčić, Derivation of a model of nonlinear micropolar plate. Ann. Univ. Ferrara Sez. VII Sci. Mat. 54 (2008) 319–333. [CrossRef] [MathSciNet]
  26. J. Tambača and I. Velčić, Existence theorem for nonlinear micropolar elasticity. ESAIM: COCV (2008) DOI: 10.1051/cocv:2008065.

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