University of Minnesota
Aerospace Engineering and Mechanics
Spring 1999 Seminar Series
The Influence of Material Instabilities at the Mesoscale on Macroscopic
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
Refreshments served after the seminar in
227 Akerman Hall.
Disability accomodations provided upon request.
Contact Kristal Belisle, Senior