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Finite element analysis of a class of stress-free martensitic microstructures

Author: Bo Li
Journal: Math. Comp. 72 (2003), 1675-1688
MSC (2000): Primary 65N30, 74N15
Published electronically: April 9, 2003
MathSciNet review: 1986799
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Abstract: This work is concerned with the finite element approximation of a class of stress-free martensitic microstructures modeled by multi-well energy minimization. Finite element energy-minimizing sequences are first constructed to obtain bounds on the minimum energy over all admissible finite element deformations. A series of error estimates are then derived for finite element energy minimizers.

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Additional Information

Bo Li
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742

Keywords: Martensitic microstructure, energy minimization, finite element deformations, error estimates
Received by editor(s): July 28, 2000
Received by editor(s) in revised form: March 15, 2002
Published electronically: April 9, 2003
Additional Notes: This work was partially supported by the NSF through grant DMS-0072958 and by the Graduate School of the University of Maryland through a GRB Summer Research Award.
Article copyright: © Copyright 2003 American Mathematical Society