Volume 34, Number 2, March/April 2000Special issue for R. Teman's 60th birthday
|Page(s)||377 - 398|
|Published online||15 April 2002|
Geometrically nonlinear shape-memory polycrystals made from a two-variant material
Courant Institute, 251 Mercer Street, New York University,
New York, NY 10012. (email@example.com)
2 Inst. für Angew. Math., Universität Bonn, Wegelerstr. 6, 53115 Bonn, Germany. (firstname.lastname@example.org)
Bhattacharya and Kohn have used small-strain (geometrically linear) elasticity to analyze the recoverable strains of shape-memory polycrystals. The adequacy of small-strain theory is open to question, however, since some shape-memory materials recover as much as 10 percent strain. This paper provides the first progress toward an analogous geometrically nonlinear theory. We consider a model problem, involving polycrystals made from a two-variant elastic material in two space dimensions. The linear theory predicts that a polycrystal with sufficient symmetry can have no recoverable strain. The nonlinear theory corrects this to the statement that a polycrystal with sufficient symmetry can have recoverable strain no larger than the 3/2 power of the transformation strain. This result is in a certain sense optimal. Our analysis makes use of Fritz John's theory of deformations with uniformly small strain.
Mathematics Subject Classification: 74B20 / 74Q20
Key words: Shape memory polycrystals / recoverable strain / nonlinear homogenization.
© EDP Sciences, SMAI, 2000
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.