# University of Minnesota

Aerospace Engineering and Mechanics

**Winter 1997 Seminar Series**

*Exact Solutions in Compressible Finite Elasticity*

__Abstract__

**The constraint of incompressibility has led to the discovery of several
exact solutions in isotropic finite elasticity, most notably the controllable or
universal solutions of Rivlin and others. Ericksen has examined the problem of
finding all such solutions. He has also proved that there are no controllable
finite deformations in isotropic compressible elasticity, except for homogeneous
deformations. **

In this talk some related questions are examined for
three special classes of compressible isotropic elastic materials, one of which
is the class of harmonic materials. Several closed form solutions, similar to
the Rivlin solutions, are obtained. In particular, some classes of controllable
deformations are obtained, e.g. some deformations possible in all harmonic
materials. The question of finding all such controllable deformations is
addressed, with rather surprising results. For instance, it is shown that every
harmonic scalar function generates a deformation that is controllable for
harmonic materials. Finally, analysis of the controllability conditions
suggests that the three classes of strain energy functions considered may be the
only ones for which results of this type can be obtained.

###
Friday, April 18, 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.