Abstract
The set of recoverable (or stress-free) strains plays a central role in the peculiar properties of shape memory alloys. New upper bounds are presented for estimating the recoverable strains of polycrystalline shape memory alloys, in the finite strains setting. Those bounds take the texture of the polycrystal (i.e., the shapes, distribution and orientations of the grains) into account. A reference two-orientation problem is studied for investigating the optimality of the bounds proposed.
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References
Bhattacharya, K.: Microstructure of martensite. Oxford Univ. Press, Oxford (2003)
Bhattacharya, K., Kohn, R.: Energy minimization recoverable strains polycrystalline shape memory alloys. Arch. Rat. Mech. Analysis 139(2), 99–180 (1997)
Shu, Y., Bhattacharya, K.: The influence of texture on the shape memory effect in polycrystals. Acta. Mater. 46, 5457–5473 (1998)
Peigney, M.: Recoverable strains in composite shape-memory alloys. J. Mech. Phys. Solid 56, 360–375 (2008)
Milton, G., Serkov, S.: Bounding the current in nonlinear conducting composites. J. Mech. Phys. Solid 48, 1295–1324 (2000)
Talbot, D.R.S., Willis, J.R.: Bounds for the effective constitutive relation of a nonlinear composite. Proc. Math. Roy. Soc. 460, 2705–2723 (2004)
Peigney, M.: A pattern-based method for bounding the effective response of a nonlinear composite. J. Mech. Phys. Solid 53, 923–948 (2005)
Dacorogna, B.: Direct methods in the calculus of variations. Springer, Berlin (1989)
Ball, J.M., James, R.D.: Proposed experimental tests of a theory of fine microstructure and the two-well problem. Phil. Trans. Roy. Soc. London A 338, 338–450 (1992)
Ball, J.M., James, R.D.: Fine phase mixtures as minimizers of energy. Arch. Rat. Mech. Analysis 100, 13–52 (1987)
Milton, G.: The theory of composites. Cambridge Univ. Press, New York (2002)
Peigney, M.: A non-convex lower bound on the effective energy of polycrystalline shape-memory alloys. J. Mech. Phys. Solid 57, 970–986 (2009)
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Peigney, M. (2012). Towards Optimal Bounds on the Recoverable Strains in Polycrystalline Shape Memory Alloys. In: Frémond, M., Maceri, F. (eds) Mechanics, Models and Methods in Civil Engineering. Lecture Notes in Applied and Computational Mechanics, vol 61. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24638-8_10
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DOI: https://doi.org/10.1007/978-3-642-24638-8_10
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