Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-10T09:47:31.636Z Has data issue: false hasContentIssue false

Microstructural Evolution and Metastability in Active Materials

Published online by Cambridge University Press:  10 February 2011

David Kinderlehrer*
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213-3890
Get access

Abstract

Metastable systems pose significant problems in both analysis and simulation. We discuss here the evolution of microstructure in a shape-memory alloy where energetic contributions from disparate scales play determining roles. This is a challenge for modelling since the finest length scales cannot be ‘seen’ at macroscopic level. We then provide a mechanism for kinetics that gives a different notion metastability.

Type
Research Article
Copyright
Copyright © Materials Research Society 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Abeyaratne, R, Chu, C, and James, R 1996, Phil. Mag. A, 73.2, 457497 Google Scholar
[2] Jordan, R, Kinderlehrer, D, and Otto, F 1997, Physica D, 107, 265271 Google Scholar
[3] Jordan, R, Kinderlehrer, D, and Otto, F 1998, Siam J Math Anal, 29, 117 Google Scholar
[4] Jordan, R, Kinderlehrer, D, and Otto, F in preparationGoogle Scholar
[5] Kinderlehrer, D 1997 in Mathematics and Control in Smart Structures, (Varadan, V.K. and Chandra, J, eds) Proc. SPIE 3039, 213 Google Scholar
[6] Bensousson, A, Lions, J-L., and Papinicolaou, G 1978 Asymptotic analysis for periodic structures, North Holland Google Scholar
[7] Ball, J.M. and James, R D. 1987, Arch. Rat. Mech. Anal. 100, 1352, 1991, Phil. Trans. Roy. Soc. Lond. A338, 389–450Google Scholar
[8] James, R and Kinderlehrer, D 1989 in PDE's and continuum models of phase transitions, (M, Rascle, Serre, D, and Slemrod, M, eds.) Lecture Notes in Physics 344, Springer, 5184.Google Scholar
[9] Bhattacharya, K 1992, Arch. Rat. Mech. Anal. 120, 201244 Google Scholar
[10] Ericksen, J.L. 1987 in Metastability and Incompletely Posed Problems, (Antman, S. Ericksen, J.L. Kinderlehrer, D. Muillereds, I) IMA Vol. Math. Appl. 3, Springer, 7796 Google Scholar
[11] Finnis, M W. and Sinclair, J E. 1984 Phil. Mag. A 50, 45 Google Scholar
[12] Sutton, A P. and Baluffi, R W. 1995 Interfaces in Crystalline Materials, Oxford 8 Google Scholar