13th International Conference on Fracture June 16-21, 2013, Beijing, China 4. Conclusions An updated Lagrangian formulation based on finite deformation theory has been established for structural analysis of deformation of hyper-elastic body including lattice defects. A few examples have been shown for the application of the geometrically non-linear deformation of hyper-elastic body including lattice defects. The results have showed that the method can be applicable to the analysis of kink deformation which had been observed experimentally in long-period stacking ordered magnesium alloy. The criterion of dislocation nucleation, short-range interaction of lattice defects, and driving force of lattice defects should be discussed in the further study. Acknowledgments This work was supported by Grants-in-Aid for Scientific Research (KAKENHI). References [1] M. Seefeldt, Disclinations in Large-strain Plastic Deformation and Work-Hardening, Rev Adv Mat Sci 2 (2001) 44-79. [2] A. Nakatani, W.J. Drugan, E. Van der Giessen, A. Needleman, Crack Tip Fields at a Ductile Single Crystal-Rigid Material Interface, Int J Fract 122 (2003) 131-159. [3] V. Taupin, L. Capolungo, C. Fressengeas, A. Das, M. Upadhyay, Grain Boundary Modeling Using an Elasto-Plastic Theory of Dislocation and Disclination Fields, J Mech Phys Solids 61 (2013), 370-384. [4] D.G.B. Edelen, A Gauge Theory of Dislocation and Disclinations, Springer-Verlag, Lecture Note in Physics, 1983. [5] J.D. Clayton, D.L. McDowell, D.J. Bammann, Modeling dislocations and disclinations with finite micropolar elastoplasticity, Int J Plasticity 22 (2006) 210-256. [6] M. Braun, Linear Elasticity with Couple Stresses, in: J.-F. Ganghoffer, F. Pastrone (eds.) Mech Microstru Solids 2, LNACM 50, Springer-Verlag Berlin Heidelberg 2010, pp.1-8. [7] L. M. Zubov, Continuum Theory of Dislocations and Disclinations in Nonlinearly Elastic Micropolar Media, Mech Solids 46 (2008), 348-356. [8] Leonid M. Zubov, Nonlinear Theory of Dislocations and Disclinations in Elastic Bodies, Springer, 1997. [9] V.S. Deshpande, A. Needleman, E. Van der Giessen, Finite strain discrete dislocation plasticity, J Mech Phys Solids 51 (2003), 2057-2083. [10] A. Acharya, C. Fressengeas, Coupled Phase Transformation and Plasticity as a Field Theory of Crystal Defects, Int J Fract 174, 87-94 (2012). -7-
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