A field theory of dislocation mechanics and plasticity is illustrated through new results at the nano, meso, and macro scales. Specifically, dislocation nucleation, the occurrence of wave-type response in quasi-static plasticity, and a jump condition at material interfaces and its implications for analysis of deformation localization are discussed.
Acharya, A.Constitutive Analysis of finite deformation field dislocation mechanics . Journal of the Mechanics and Physics of Solids, 52, 301-316 (2004).
2.
Acharya, A. and Roy, A.Size effects and idealized dislocation microstructure at small scales: predictions of a phenomenological model of Mesoscopic Field Dislocation Mechanics: Part I, Journal of the Mechanics and Physics of Solids, 54, 1687-1710 (2006).
3.
Acharya, A.Driving forces and boundary conditions in continuum dislocation mechanics , Proceedings of the Royal Society A, 459, 1343-1363 (2003).
4.
Miller, R. and Acharya, A.A stress-gradient based criterion for dislocation nucleation in crystals . Journal of Mechanics and Physics of Solids, 52, 1507-1525 (2004).
5.
Acharya, A.Jump condition for GND evolution as a constraint on slip transmission at grain boundaries, Philosophical Magazine A, 1349-1359 (2007 ).
6.
Acharya, A.A model of crystal plasticity based on the theory of continuously distributed dislocations, Journal of the Mechanics and Physics of Solids , 49, 761-784 (2001).
7.
Roy, A. and Acharya, A.Finite element approximation of field dislocation mechanics, Journal of the Mechanics and Physics of Solids , 53, 143-170 (2005).
8.
Limkumnerd, S. and Sethna, J.P.Mesoscale theory of grains and cells: crystal plasticity and coarsening, Physical Review Letters, 96, 095503 (2006).
9.
Limkumnerd, S. and Sethna, J.P. Stress-free states of continuum dislocation fields: Rotations, grain boundaries, and the Nye dislocation density tensor, Physical Review B, 75, 224121 (2007 ).
10.
Limkumnerd, S. and Sethna, J.P.Shocks and slip systems: predictions from a theory of continuum dislocation dynamics. (submitted) available at http://arxiv.org/abs/cond-mat/0610641 (2006 ).
11.
Kröner, E.Continuum theory of defects, in Physics of Defects , pp. 217-315, ed. R. Balian et al., North-Holland , Amsterdam, 1981.
12.
Mura, T.Micromechanics of Defects in Solids, Springer, Berlin, 1989.
13.
Head, A.K. , Howison, S.D., Ockendon , J.R., and Tighe, S.P.An equilibrium theory of dislocation continua . SIAM Review, 35, 580-609 (1993).
14.
Miller, R.E. , and Rodney, D.On the nonlocal nature of dislocation nucleation during nanoindentation. Journal of the Mechanics and Physics of Solids, 56, 1203-1223 (2008 ).
15.
Ercolessi, F. and Adams, J.Interatomic potentials from first-principles calculations-the force-matching method. Europhysics Letters , 26, 583 (1994).
16.
Kelchner, C.L., Plimpton, S. and Hamilton, J.Dislocation nucleation and defect structure during surface indentation. Physical Review B, 58, 11085-11088 (1998 ).
17.
Knap, J. and Ortiz, M.An analysis of the quasicontinuum method. Journal of the Mechanics and Physics of Solids, 49, 1899-1923 (2001 ).
18.
Li, J. , van Vliet, K., Zhu , T., Yip , S. and Suresh, S.Atomistic mechanisms governing elastic limit and incipient plasticity in crystals. Nature, 418, 307-310 (2002).
19.
Miller, R.E. , Shilkrot, L.E. and Curtin, W.A coupled atomistic and discrete dislocation plasticity simulation of nano-indentation into single crystal thin films. Acta Materiala, 52, 271-284 (2003).
20.
Shenoy, V.B. , Miller, R., Tadmor , E., Rodney, D., Phillips, R. and Ortiz, M.An adaptive methodology for atomic scale mechanics: The quasicontinuum method. Journal of the Mechanics and Physics of Solids, 47, 611-642 (1999).
21.
Tadmor, E.B. and Miller, R.E.Quasicontinuum method website. www.qcmethod.com (accessed 2007).
22.
van Vliet, K. and Suresh, S.Simulations of cyclic normal indentation of crystal surfaces using the bubble-raft model. Philosophical Magazine A, 82, 1993-2001 (2002).
23.
Knap, J. and Ortiz, M.Effect of indenter-radius size on Au(001) nanoindentation. Physical Review Letters, 90, 226102 (2003).
24.
van Vliet, K.J., Li, J., Zhu , T., Yip , S. and Suresh, S.Quantifying the early stages of plasticity through nanoscale experiments and simulations. Physical Review B, 67, 104105 (2003).
25.
Li, J.The mechanics and physics of defect nucleation . Materials Research Bulletin, 32, 151-159 (2007).
26.
Nix, W. and Gao, H.Indentation size effects in crystalline materials: a law for strain gradient plasticity. Journal of the Mechanics and Physics of Solids, 46, 411-425 (1998).
27.
Gerberich, W., Tymiak, N., Grunlan , J., Horstemeyer, M. and Baskes, M.Interpretations of indentation size effects . Journal of Applied Mechanics , 69, 433-442 (2002).
28.
Dupuy, L., Tadmor, E., Miller, R. and Phillips, R.Finite temperature quasicontinuum: Molecular dynamics without all the atoms . Physical Review Letters, 95, 060202 (2005 ).
29.
Babic, M.Average balance equations for granular materials. International Journal of Engineering Science, 35, 523-548 (1997).
30.
Roy, A. and Acharya, A.Size effects and idealized dislocation microstructure at small scales: predictions of a phenomenological model of Mesoscopic Field Dislocation Mechanics: Part II. Journal of the Mechanics and Physics of Solids, 54, 1711-1743 (2006).
31.
Jiang, B.The least-squares finite element method, in Theory and Computation in Fluid Dynamics and Electromagnetics, Springer Series in Scientific Computation , Springer, Berlin, 1998.
32.
Machová, A.Stress calculations on the atomistic level. Modelling and Simulation in Materials Science and Engineering, 9, 327-337 (2001).
33.
Nielsen, O.H. and Martin, R.M.Quantum-mechanical theory of stress and force. Physical Review B, 32, 3780- 3791 (1985).
34.
Lutsko J. F.Stress and elastic constants in anisotropic solids: molecular dynamics techniques . Journal of Applied Physics, 64, 11524 (1988 ).
35.
Hardy, R.J.Formulas for determining local properties in molecular-dynamics simulations: shock waves. Journal of Chemical Physics, 76, 6228 (1982).
36.
Irving, J.H. and Kirkwood J.G.The statistical mechanical theory of transport processes: IV. The equations of hydrodynamics. Journal of Chemical Physics, 18, 81729 (1950).
37.
Tsai, D.H.The virial theorem and stress calculation in molecular dynamics. Journal of Chemical Physics, 70, 137582 (1979).
38.
Maranganti, R., Sharma, P. and Wheeler, P.Quantum notions of stress. ASCE Journal of Aerospace Engineering, 20, 22-37 (2007).
39.
Zuev, L.B.On the waves of plastic flow localization in pure metals and alloys. Annalen der Physik, 16, 286-310 (2007).
40.
Kocks U.F., 1981. Kinetics of nonuniform deformation, in: Progress in Materials Science, Chalmers anniversary volume, p. 185, Pergamon , Oxford, 1981.
41.
Ziegenbein, A. , Achmus, Ch. , Plessing, J. and Neuhäuser, H.On Lüders band formation and propagation in CuAl and CuMn single crystals, in Plastic and Fracture Instabilities in Materials, pp. 101-119, ASME AMD-Vol. 200/MD-Vol. 57, 1995.
42.
Brenner, S.S.Plastic deformation of copper and silver whiskers. Journal of Applied Physics, 28, 1023-1026 (1957).
43.
Nittono, O.X-ray topographic studies on the Lüders band propagation and the dislocation motion in copper whisker crystals. Japanese Journal of Applied Physics, 10, 188-196 (1971).
44.
Saimoto, S.Personal communication in reference to "The deformation of copper whiskers", MSc. Thesis, University of British Columbia , Vancouver, BC, 1960.
45.
Gotoh, Y.Slip patterns of copper whiskers subjected to tensile deformation. Physica Status Solidi (a), 24, 305-313 (1974).
46.
Varadhan, S., Beaudoin, A.J. and Fressengeas , C.Coupling the dynamics of statistically distributed and excess dislocations. Proceedings of Science, http://pos.sissa.it/archive/conference/023/004/SMPRI2005_004.pdf (2005).
47.
Acharya, A. and Beaudoin, A.J.Grain-size effect in polycrystals at moderate strains. Journal of the Mechanics and Physics of Solids, 48, 2213-2230 (2000).
48.
Taupin, V. , Varadhan, S., Chevy , J., Fressengeas, C., Beaudoin, A.J., Montagnat, M. and Duval, P.Effects of size on the dynamics of dislocations in ice single crystals. Physical Review Letters, 99, 155507 (2007).
49.
Varadhan, S., Beaudoin, A.J., Acharya , A. and Fressengeas , C.Dislocation transport using and explicit Galerkin/leastsquares formulation. Modelling and Simulation in Materials Science and Engineering, 14, 1245-1270 (2006).
50.
Mura, T.Continuous distribution of moving dislocations. Philosophical Magazine, 89, 843-857 (1963).
Truesdell, C.A. and Toupin, R.A. in Principles of Classical Mechanics and Field Theory, Encyclopedia of Physics, Vol. III/1, pp. 226-790, ed. S. Flügge, Springer, Berlin, 1960.
