# University of Minnesota

Aerospace Engineering and Mechanics

**Spring 1999 Seminar Series**

*Entropic Elasticity of Martensites*

*Abstract*

### In a typical strain test, shape memory wires exhibit a characteristic
hardening on the stage of microstructure development. In experiments, the
degree of hardening is often related to the defectiveness or the inhomogeneity
of the sample. We suggest a new interpretation of the hardening in martensites
as the effect of entropic, rubber-like elasticity. We assume that the sample
can be represented as an ensemble of ideal sub-samples and adopt a canonical
distribution which introduces a new parameter with the dimension of
temperature. This parameter characterizes the degree of defectiveness of the
sample. At zero effective temperature we recover the results of the classical
energy minimization. At finite temperatures the usual statistical averaging
produces the desired hardening as a result of strain dependence of the
configurational entropy. This effect is intimately related to the non-convexity
of the energy and is absent if the energy is quadratic.

### Friday, May 7, 1999

209 Akerman
Hall

2:30-3:30 p.m.

### Refreshments served after the seminar in
227 Akerman Hall.

Disability accomodations provided upon request.

Contact Kristal Belisle, Senior
Secretary, 625-8000.