Perry H. Leo, Associate Fellow
John S. Lowengrub, Co-Principal Investigator

Computational Problems in Multi-Component/Multi-Phase Elastic Materials

This research group continues its investigation of microstructures formed in crystalline alloys using a dual approach with sharp and diffuse interface methods. A main focus of this study is to develop a threedimensional sharp interface model to study equilibrium shapes, morphological instabilities (particle splitting), and multi-particle coarsening. A secondary focus will be to include multicomponent diffusion, multiple phases, and kinetics in both diffuse and sharp interface models. These features are needed to include solid-state reactions in the transformation models.

A past study conducted by this research group demonstrated that a morphological instability driven by deviatoric applied stresses can generate elastically-induced particle splitting. The splitting occurs when the elastic fields are above some critical value. Below this value one observes a small perturbation consistent with the splitting, but the perturbation is stabilized by surface tension. Ongoing work includes developing a three-dimensional boundary integral method to track precipitate motion. Progress has been made in finding equilibrium shapes for three-dimensional particles and investigating the morphological stability of a particle. In particular, the group has found that concave shapes can be generated by external fluxes; these shapes may lead to particle splitting as described above.

Research Group and Collaborator

Vittorio Cristini, Supercomputing Institute Research Scholar
Shuwang Li, Graduate Student Researcher
Qing Nie, Department of Mathematics, University of California at Irvine, Irvine, California
Nicolas Vera, Graduate Student Researcher
Hua Zhou, Research Associate