Continua with microstructure: Cosserat theory

7. References

• Biot , M. A. 1967 . “Rheological stability with couple stresses and its application to geological folding” . Proc. Royal Society A , 298 : 402 – 423 .
   Google Scholar
• Cauchy , A. L. 1851 . «Note sur l'équilibre et les mouvements vibratoires des corps solides» . Comptes-rendus , 32 : 323 – 326 .
   Google Scholar
• Cosserat , E. and Cosserat , F. 1909 . Théorie de corps déformables Paris : Hermann et Fils . English translation by Delphenich D. Theory of Deformable Bodies 2007
   Google Scholar
• Günther , W. 1958 . Zur Statik und Kinematik des Cosseratschen Kontinuums. Abhandlungen der Braunschweigischen Wissenschaftlichen Gesellschaft Vol. 10 , 195 – 213 .
   Google Scholar
• Eringen , A. C. 1970 . Foundations of Micropolar Thermoelasticity Springer . Wien
   Google Scholar
• Forest , S. 2002 . “Homogenization methods and the mechanics of generalized continua—Part 2” . Theoretical and Applied Mechanics , : 113 – 143 .
   Google Scholar
• Grad , H. 1952 . “The profile of a steady plane shock wave” . Communications on Pure and Applied Mathematics , 5 ( n° 5 ) : 257 – 300 .
   Google Scholar
• Kröner , E. 1968 . Mechanics of gGeneralized Continua New York : Springer .
   Google Scholar
• Kunin , I. A. 1982 . “Elastic media with microstructure I: One-dimensional models (eds. ” . In Springer Series in Solid State Sciences Springer-Verlag Edited by: Cardona , M , Fulde , P , Queisser , H-J and Kröner , E . Vol. 26 ,
   Google Scholar
• Kunin , I. A. 1983 . “Elastic media with microstructure II: Three-dimensional models (eds. ” . In Springer Series in Solid State Sciences Springer-Verlag Edited by: Cardona , M. , Fulde , P. , Queisser , H.-J. and Kröner , E. Vol. 44 ,
   Google Scholar
• Lakes , R. S. 1998 . “Elastic freedom in cellular solids and composite materials” . In Mathematics of Multiscale Materials , IMA 99 Edited by: Golden , K . 129 – 153 . Springer .
   Google Scholar
• Lakes , R. S. 2010 . Cosserat Elasticity; micropolar elasticity , http://silver.neep.wisc.edu/∼lakes/Coss.html/
   Google Scholar
• Mindlin , R. D. 1963 . “Influence of couple-stresses on stress-concentrations” . Experimental Mechanics , 3 : 1 – 7 .
   Google Scholar
• Mindlin , R. D. 1964 . “Microstructure in linear elasticity” . Archive for Rational Mechanics and Analysis , 16 ( n° 1 ) : 51 – 78 . doi:10.1007,/BF00248490
   Google Scholar
• Mühlhaus , H.-B. and Vardoulakis , I. 1987 . “The thickness of shear bands in granular materials” . Géotechnique , 37 : 271 – 283 .
   Google Scholar
• Neff , P. 2010 . Cosserat Theory , http://www.uni-due.de/mathematik/ag_neff/cosserat/
   Google Scholar
• Stojanovic , R. 1970 . Recent Developments in the Theory of Polar Continua CISM 27, Springer
   Google Scholar
• Sulem , J. and Vardoulakis , I. 1990 . “Bifurcation analysis of the triaxial test on rock specimens” . Acta Mechanica , 83 : 195 – 212 .
   Google Scholar
• Vardoulakis , I. 1989 . “Shear banding and liquefaction in granular materials on the basis of a Cosserat continuum theory” . Ingenieur Archiv. , 59 : 106 – 113 .
   Google Scholar
• Vardoulakis , I. 2009 . Lectures on Cosserat continuum mechanics with application to the mechanics of granular media, MEDIGRA, EU Ideas Program, ERC-2008-AdG 228051
   Google Scholar
• Vardoulakis , I. and Sulem , J. 1995 . Bifurcation Analysis in Geomechanics Glasgow : Blackie Academic & Professional .
   Google Scholar
• Voigt , W. 1887 . Theoretische Studien über die Elastizität der Kristalle. Abbh. Wiss. Ges. Göttingen
   Google Scholar
• Voigt , W. 1894 . Über Medien ohne innere Kräfte und eine durch die gelieferte mechanische Deutung der Maxwell-Herzschen Gleichungen. Abbh. Wiss. Ges. Göttingen 72 – 79 .
   Google Scholar