Simple criterion for the existence of rank-one connections between martensitic wells

Journal of Elasticity

Volumn 57, Issue 3, 1999, Pages 281-305

  Forclaz, Alain ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; MARTENSITE; MATRIX ALGEBRA; TWINNING; VECTORS;

COMPOUND TWINS; MARTENSITIC WELLS; RANK ONE CONNECTION;

ELASTICITY;

EID: 0033284152     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007697701944     Document Type: Article

References (25)

1. J.M. Ball and R.D. James, Fine phase mixtures as minimizers of energy. Arch. Rational Mech. Anal. 100 (1987) 13-52.
2. J.M. Ball and R.D. James, Proposed experimental tests of a theory of fine microstructure and the two-well problem. Philos. Trans. Roy. Soc. London Ser. A 338 (1992) 389-450.
3. K. Bhattacharya, Self-accommodation in martensite. Arch. Rational Mech. Anal. 120 (1992) 201-244.
4. K. Bhattacharya, Theory of martensitic micro structure and the shape memory effect. In: G. Airoldi, I. Müller and S. Miyasaki (eds), Shape Memory Alloys: From Microstructure to Macroscopic Properties. Trans. Tech. Publications (1997).
5. K. Bhattacharya and G. Dolzmann, Relaxation of some multi-wells problems. Preprint (1999).
6. J.L. Ericksen, Theory of stress-free joints. J. Elasticity 13 (1983) 3-15.
7. J.L. Ericksen, On kinematic conditions of compatibility. J. Elasticity 26 (1991) 65-74.
8. M.E. Gurtin, Two-phase deformations of elastic solids. Arch. Rational Mech. Anal. 84 (1983) 1-29.
9. P.R. Halmos, Finite-dimensional Vector Spaces, 2nd edn. Van Nostrand, Princeton (1958).
10. K.F. Hane, Microstructure in thermoelastic martensites. PhD Thesis, University of Minnesota, USA (1997).
11. K.F. Hane and T.W. Shield, Microstructure in the cubic to monoclinic transition in Titanium-Nickel shape memory alloys. Acta Materialia 47 (1999) 2603-2617.
12. B. Hertog, The elastic dielectric: Minimizing states in ferroelectrics. PhD Thesis, University of Minnesota, USA (1987).
13. R.D. James and K.F. Hane, Martensitic transformations and shape-memory alloys. Acta Materialia 48 (2000) 197-222.
14. A.G. Khachaturyan, Theory of Structural Transformations in Solids. Chichester, New York (1983).
15. S. Müller, Variational Models for Micro structure and Phase Transitions. Lecture Notes no. 2. Preprint MPI Leipzig (1998).
16. B. Ou, On a kinematic compatibility equation related to elastic stress-free joints and crystal twins. J. Elasticity 45 (1996) 73-89.
17. G.P. Parry and M. Silhavỳ, On rank one connectedness, for planar objective functions. Preprint (1999).
18. M. Pitteri, On type-2 twins in crystals. Internat. J. Plasticity 2 (1986) 99-106.
19. M. Pitteri and G. Zanzotto, Generic and non-generic cubic-to-monoclinic transitions and their twins. Acta Materialia 46 (1997) 225-237.
20. M. Silhavỳ, The Mechanics and Thermodynamics of Continuous Media. Springer, Berlin (1997).
21. M. Silhavỳ, Rank-one perturbations of deformation gradients. Preprint (1998).
22. M. Silhavỳ, On the compatibility of wells. J. Elasticity 55 (1999) 11-17.
23. N.K. Simha, Twin and habit plane microstructures due to the tetragonal to monoclinic transformation in zirconia. J. Mech. Phys. Solids 45 (1997) 261-292.
24. D. Soligo, G. Zanzotto and M. Pitteri, Non-generic concentrations for shapememory alloys; the case of CuZnAl. Acta Materialia 47 (1999) 2741-2750.
25. P.B. Yale, Geometry and Symmetry. Dover, New York (1988).