Kinetics of phase transformations in the peridynamic formulation of continuum mechanics

Journal of the Mechanics and Physics of Solids

Volumn 54, Issue 9, 2006, Pages 1811-1842

  Dayal, Kaushik ^a   Bhattacharya, Kaushik ^a  

^a California Institute of Technology   (United States)

Author keywords

Microstructures; Peridynamics; Phase transformation; Shape memory effect; Stability and bifurcation

Indexed keywords

ACOUSTIC WAVES; BIFURCATION (MATHEMATICS); CRACKS; EDGE DETECTION; INTERFACES (MATERIALS); MARTENSITE; NUCLEATION; PHASE TRANSITIONS; PROBLEM SOLVING; SHAPE MEMORY EFFECT; THERMODYNAMIC PROPERTIES;

CLASSICAL CONTINUUM THEORY; DYNAMIC INSTABILITY; PERIDYNAMIC FORMULATION; PERIDYNAMICS; PHASE BOUNDARIES; STABILITY AND BIFURCATION;

CONTINUUM MECHANICS;

EID: 33745173426     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2006.04.001     Document Type: Article

References (29)

1. Abeyaratne R., and Knowles J.K. On the driving traction on a surface of a strain discontinuity in a continuum. J. Mech. Phys. Solids 38 (1990) 345-360
2. Abeyaratne R., and Knowles J.K. Implications of viscosity and strain gradient effects for the kinetics of propagating phase boundaries in solids. SIAM J. Appl. Math. 51 5 (1991) 1205-1221
3. Abeyaratne R., and Knowles J.K. Kinetic relations and the propagation of phase boundaries in solids. Arch. Ration. Mech. Anal. 114 (1991) 119-154
4. Anderson E., Bai Z., Bischof C., Blackford S.L., Demmel J.W., Dongarra J.J., DuCroz J., Greenbaum A., Hammarling S., McKenney A., and Sorensen D. LAPACK User's Guide. third ed. (1999), Society for Industrial and Applied Mathematics.
5. Artemev A., Jin Y., and Khachaturyan A. Three-dimensional phase field model of proper martensitic transformation. Acta Mater. 49 7 (2001) 1165-1177
6. Ball, J.M., James, R.D., 2005. Metastability in martensitic phase transformations. In preparation.
7. Bhattacharya K. Microstructure of Martensite (2003), Oxford University Press, Oxford
8. Christian J.W. The Theory of Transformations in Metals and Alloys (1975), Pergamon, New York
9. Dondl P.W., and Zimmer J. Modeling and simulation of martensitic phase transitions with a triple point. J. Mech. Phys. Solids 52 9 (2004) 2057-2077
10. Engl H.W., Hanke M., and Neubauer A. Regularization of Inverse Problems (2000), Kluwer Academic Publishers, Dordrecht
11. Eshelby, J.D., 1956. Solid State Physics, vol. 3. Academic Press, New York, pp. 17-144.
12. Eshelby J.D. The elastic energy-momentum tensor. J. Elasticity 5 (1975) 321-335
13. James, R.D., 2005. Unpublished micrographs.
14. Killough, M.G., 1998. A diffuse interface approach to the development of microstructure in martensite. Ph.D. Thesis, New York University.
15. Kloucek P., and Luskin M. Computational modeling of the martensitic transformation with surface energy. Math. Comput. Model. 20 (1994) 101-121
16. Kunin, I.A., 1982. Elastic media with microstructure. Springer Series in Solid-State Sciences, vol. 26. Springer, Berlin.
17. Lefloch P. Propagating phase boundaries: formulation of the problem and existence via the Glimm method. Arch. Ration. Mech. Anal. 123 (1993) 153-197
18. Lei Y., Friswell M.I., and Adhikari S. A Galerkin method for distributed systems with non-local damping. Int. J. Solids Struct. 43 (2006) 3381-3400
19. Olson, G.B., Roitburd, A.L., 1992. Martensitic nucleation. In: Martensite. ASM, pp. 149-174 (Chapter).
20. Porter D., and Stirling D.G.S. Integral Equations (1990), Cambridge University Press, Cambridge
21. Purohit, P.K., 2001. Dynamics of phase transitions in strings, beams and atomic chains. Ph.D. Thesis, California Institute of Technology.
22. Silling S.A. Reformulation of elasticity theory for discontinuities and long-range forces. J. Mech. Phys. Solids 48 (2000) 175-209
23. Silling, S.A., Kahan, S., 2004. Peridynamic modeling of structural damage and failure. In: Conference on High Speed Computing, Gleneden Beach, Oregon, USA.
24. Silling S.A., Zimmermann M., and Abeyaratne R. Deformation of a peridynamic bar. J. Elasticity 73 (2003) 173-190
25. Truskinovsky, L., 1993. Kinks versus shocks. In: Fosdick, R., Dunn, E., Slemrod, M. (Eds.), Shock Induced Transitions and Phase Structures in General Media, IMA, vol. 52. Springer, Berlin.
26. Truskinovsky L., and Vainchtein A. Kinetics of martensitic phase transitions: lattice model. SIAM J. Appl. Math. 66 2 (2005) 533-553
27. Wang, Y.Z., Chen, L.Q., Khachaturyan, A.G., 1994. Computer simulation of microstructure evolution in coherent solids. In: Solid-Solid Phase Transformations. The Minerals Metals and Material Society, pp. 245-265 (Chapter).
28. Weckner O., and Abeyaratne R. The effect of long-range forces on the dynamics of a bar. J. Mech. Phys. Solids 53 (2005) 705-728
29. Zimmermann, M., 2002. Phase transformations in the one dimensional peridynamic theory. Unpublished private communication.