University of Minnesota
Aerospace Engineering and Mechanics
Spring 1999 Seminar Series

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

Prof. David Owen

Department of Mathematics, Carnegie Mellon University


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.