A multilattice quasicontinuum for phase transforming materials: Cascading Cauchy Born kinematics

Journal of Computer-Aided Materials Design

Volumn 14, Issue SUPPL. 1, 2007, Pages 219-237

  Dobson, M ^a   Elliott, R S ^a   Luskin, M ^a   Tadmor, E B ^a,b  

^a UNIVERSITY OF MINNESOTA   (United States)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Cascading Cauchy Born; Finite elements; Multilattice; Multiscale; Quasicontinuum

Indexed keywords

CONTINUUM DAMAGE MECHANICS; CRYSTAL STRUCTURE; DEFORMATION; KINEMATICS; ONE DIMENSIONAL; PHASE TRANSITIONS; PHONONS;

CASCADING CAUCHY-BORN; PHONON STABILITY ANALYSIS; QUASICONTINUUM;

COMPUTATIONAL METHODS;

EID: 43249092140     PISSN: 09281045     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10820-007-9084-7     Document Type: Conference Paper

References (17)

1. Tadmor E.B., Ortiz M. and Phillips R. (1996). Quasicontinuum analysis of defects in solids. Phil. Mag. A 73: 1529-1563
2. Shenoy V.B., Miller R., Tadmor E.B., Rodney D., Phillips R. and Ortiz M. (1999). An adaptive finite element approach to atomic-scale mechanics: the Quasicontinuum method. J. Mech. Phys. Solids 47: 611-642
3. Miller R.E. and Tadmor E.B. (2002). The quasicontinuum method: overview, applications and current directions. J. Comput-Aid. Mat. Des. 9: 203-239
4. Born M. and Huang K. (1954). Dynamical Theory of Crystal Lattices. Clarendon Press, Oxford
5. Pitteri M. (1985). On the kinematics of mechanical twinning in crystals. Arch. Rat. Mech. Anal. 88: 25-57
6. Zanzotto G. (1988). Twinning in minerals and metals: remarks on the comparison of a thermoelastic theory with some available experimental results: notes I and II. Atti Accademia Nazionale dei Lincei, Rend. Fis. 82: 725742 and 743756
7. Tadmor E.B., Smith G.S., Bernstein N. and Kaxiras E. (1999). Mixed finite element and atomistic formulation for complex crystals. Phys. Rev. B 59: 235-245
8. Smith G.S., Tadmor E.B. and Kaxiras E. (2000). Multiscale simulation of loading and electrical resistance in silicon nanoindentation. phys. Rev. Lett. 84: 1260-1263
9. 3: an ab initio finite element simulation. Acta Mater. 50: 2989-3002
10. Zanzotto G. (1992). On the material symmetry group of elastic crystals and the born rule. Arch. Rational Mech. Anal. 121: 1-36
11. Zanzotto G. (1996). The cauchy-born hypothesis, nonlinear elasticity and mechanical twinning in crystals. Acta Cryst. A 52: 839-849
12. Elliott R.S., Triantafyllidis N. and Shaw J.A. (2006). Stability of crystalline solids-I: continuum and atomic lattice considerations. J. Mech. Phys. Solids 54: 161-192
13. Elliott R.S., Shaw J.A. and Triantafyllidis N. (2006). Stability of crystalline solids-II: application to temperature-induced martensitic phase transformations in a bi-atomic crystal. J. Mech. Phys. Solids 54: 193-232
14. Dobson, M., Luskin, M.: Analysis of a force-based quasicontinuum approximation. arXiv:math.NA/0611543 (2006)
15. Elliott, R.S.: Multiscale bifurcation and stability of multilattices. J. Comput-Aid. Mat. Des. (2007) doi: 10.1007/s10820-007-9075-8
16. Yip, S., Li, J., Zhu, T.: Atomistic measures of strength, deformation and reactivity: toward multiscale modeling of chemo-mechanical phenomena. Proceedings of the Third International Conference on Multiscale Materials Modeling, Freiburg, September 18-22, pp. 816 (2006)
17. Dobson, M., Elliott, R.S., Tadmor, E.B.: A quasicontinuum for complex crystals. Proceedings of the Third International Conference on Multiscale Materials Modeling, Freiburg, September 18-22, pp. 889-896 (2006)