# University of Minnesota

Aerospace Engineering and Mechanics

**Fall 1996 Seminar Series**

*Damage. Gradient of Damage: A Macro-Micro Effect*

## Dr. Michel Frémond

### Laboratoire des Matériaux et
des Structures du Génie Civil

#### Champs sur Marne, France

__Abstract__

**Damage, for instance damage of concrete, results from microscopic
motions. Our basic idea is that the power of those microscopic motions must be
accounted for in a predictive theory. Thus, we decide to modify the expression
of the power of the internal forces and assume that this power depends on the
damage rate and its gradient which are related to the microscopic motions. The
models issued from this formulation are free of spurious mesh sensitivity and
are able, when compared to experimental results, to predict correctly the
behavior of some concrete structures. It results also in a good prediction of
the structural size effect which is particularly important in civil engineering.
**

**Because the theory is based on the idea that damage is produced by
microscopic motions, one can ask: What occurs when macroscopic motions become
microscopic and vanish? It is shown in an example, that the source of damage
due to macroscopic deformations vanishes and is replaced by a microscopic source
of damage. Both of them are established by the same amount of external work.
Thus there is continuity when going from macroscopic motions to microscopic
ones.
**

###
Friday, October 18, 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.