*Int.J.Sol.Struct.* **49**, 2848-2853, 2012

### MODELING AND SIMULATION OF RELAXATION IN VISCOELASTIC OPEN
CELL MATERIALS AND STRUCTURES

H.E. Pettermann, J. Hüsing

Institute of Lightweight Design and Structural
Biomechanics,

TU Wien,
Vienna, Austria

**Abstract** -
Open cell materials with cubic anisotropy and structures made thereof are
investigated with respect to their linear viscoelastic properties, in
particular their relaxation behavior.
The study is concerned with the prediction of the effective behavior which
results from the isotropic bulk material properties as well as the cellular
architecture.
Finite Element Method simulations of three-dimensional structures are employed
to predict the effective response to a wide range of loading modes in the time
domain.
For predicting the properties of the cellular materials and structures by the
Finite Element Method different modeling strategies are employed.
The first approach is a periodic unit cell method modeling an infinite medium
by means of periodic boundary conditions.
This way the entire effective linear viscoelastic constitutive behavior can be
computed.
However, it is not possible to capture effects as being attributed to traction
free faces and load introduction in specimens or structures.
A second approach follows to account for these effects by generating finite
sample models to represent situations which occur in experimental testing.
Finally, an analytical constitutive material law is developed to model linear
viscoelasticity for cubic anisotropy in the time domain.
It is implemented into the commercial Finite Element software ABAQUS/Standard
and the material parameters are gained from the unit cell investigations.
This enables the simulation of structures, parts, and components which consist
or contain such cellular materials.

(hjb,120904)