We report results on a finite element simulation of a needle-like martensitic microstructure observed in biaxial loading experiments conducted by Chu and James on single crystals of the shape-memory alloy Cu-14 at.% Al-3.9 at.% Ni. This microstructure was observed near an interface between twinned layers of two variants and a pure variant of martensite. We used a geometrically nonlinear theory of martensite to model and compute the complex microstructure by energy minimization with a boundary condition that is compatible with the microstructure. Our computational model has yielded multiple metastable states that depend on the initial state of our energy-minimizing iteration. The simulated twinned layers form branches and bend as they approach the laminate-single variant interface in good agreement with the experiment of Chu and James.
Bibliographical noteFunding Information:
We thank R. James and R. Kohn for many helpful discussions, and C. Chu and R. James for providing Fig. 1 . This work was supported in part by NSF DMS 95-05077, by AFOSR F49620-98-1-0433 and AF/F 49620-96-1-0212, by ARO DAAG55-98-1-0335, by ARPA/URI/ONR N00014-92-J-1890, by the Institute for Mathematics and Its Applications, and by the Minnesota Supercomputer Institute.
- Finite element method