# University of Minnesota

Aerospace Engineering and Mechanics

**Fall 1996 Seminar Series**

*Anti-plane Shear: An Intriguing Mathematical Model in
Solid Mechanics*

### Wills Johnson Professor of Applied Mathematics and Mechanics

School of Engineering and Applied Science,
University of
Virginia

**The intent of this expository lecture is to draw attention to an
interesting two-dimensional mathematical model arising in solid mechanics
involving a single second-order linear or quasilinear partial differential
equation. This model has the virtue of relative mathematical simplicity without
loss of essential physical relevance. Anti-plane shear deformations are one of
the simplest classes of deformations that solids can undergo. In anti-plane
shear (or longitudinal shear, generalized shear) of a cylindrical body, the
displacement is parallel to the generators of the cylinder and is independent of
the axial coordinate. This is the Mode III fracture mode for crack problems.
In recent years, considerable attention has been paid to the analysis of
anti-shear deformations within the context of various constitutive theories
(linear and nonlinear) of solid mechanics. Such studies were largely motivated
by the promise of relative analytic simplicity compared with plane problems
since the governing equations are a single second-order linear or quasilinear
partial differential equation rather than higher order or coupled systems of
partial differential equations. Thus the anti-plane shear problem plays a
useful role as a pilot problem, within which various aspects of solutions in
solid mechanics may be examined in a particularly simple setting. In this
lecture, recent developments on these issues are described for both linear and
nonlinear solid mechanics.
**

###
Friday, November 1, 1996

209 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.