# University of Minnesota

Aerospace Engineering and Mechanics

**Winter 1997 Seminar Series**

*Modeling of Microstructure in Elastically Stressed
Solids*

__Abstract__

**We study the microstructures produced by solid-state diffusional phase
transformations in two dimensions. The microstructure consists of arbitrarily
shaped precipitates embedded coherently in an infinite elastic matrix. This is
the problem that Perry Leo discussed some weeks ago. We consider two distinct
approaches. The first is a sharp interface method (discussed in brief by Leo
in his talk), where the the composition and elastic fields are calculated by
using a boundary integral method, and the precipitate-matrix interface is
tracked explicitly. The second is a diffuse interface (Cahn-Hilliard) model,
where microstructure is captured by the evolution of smooth composition and
displacement fields in which internal layers mark the precipitate-matrix
interfaces. We discuss both formulations, and show that in the limit of a sharp
interface the diffuse interface and sharp interface formulations match exactly.
We also consider the numerical implementation of the two models, and we present
results comparing precipitate shapes and motions for the two approaches.
Finally, we show that elastic inhomogeneity (i.e., different elastic constants
for the precipitate and matrix) has an important effect on the microstructures
seen in the simulations.
**

###
Friday, February 14, 1997

225 Akerman Hall, 2:30 - 3:30 p.m.

#### Refreshments served after each seminar in
227 AKERMAN HALL .

Disability accommodations provided upon request.

Contact
Leslie Petrus : Secretarial Assistant.

*petrus@aem.umn.edu* (612) 625-8000.