# University of Minnesota

Aerospace Engineering and Mechanics

**Spring 1999 Seminar Series**

*The Influence of Material Instabilities at the Mesoscale on Macroscopic
Material Response *

*Abstract*

### Structured deformations are mathematical tools for describing geometrical
changes in a body that occur at more than one length scale. These deformations
provide additional geometrical variables that can enter into constitutive
equations. In this talk, I will define and give examples of structured
deformations, describe recent results on representing the free energy of a body
undergoing a structured deformation, and show how the problem of minimizing the
Gibbs free energy in a structured deformation is related to determining the
macroscopic response of the body. Examples of constitutive equations for bodies
undergoing crystallographic slip and for bodies undergoing shear-induced
dilatation will be derived: the derived macroscopic response exhibits yielding
and hysteresis in the example of slip and reproduces Coulumb friction in the
example of shear-induced dilatation. The dissipative mechanism in each of the
two examples is that of material instabilities at the mesoscale.

### Friday, April 23, 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.