Numerische Homogenisierungsstrategien im Rahmen erweiterter Kontinua (DU 405/2-2)

The aim of the project is to model the macroscopic behaviour of cellular materials
based on the inherent microscopical properties. This results in generalised con-
tinua of micromorphic type. To solve this highly nonlinear problem, a combination
of two FE-codes is applied:

• PANDAS: a finite element package designed for multiphase materials, www.get-pandas.com.

• AdhoC⁴: a higher-order finite element code for solid mechanics.

PANDAS is used on the macroscale. For this it is continously enhanced by extended
macro theories during this project. AdhoC⁴ will serve as a solver for the microscopic
problem. It is based on standard continuum higher-order finite elements allowing
for an anisotropic Ansatz where each component of the displacement field can be
chosen individually. With these elements the beam-like structures on the micro-
level can be discretised efficiently, i.e. by using a high polynomial degree p in longi-
tudinal direction while the polynomial degree q in thickness direction can be lower.
Both programs work in a partitioned solution approach (i.e. exchanging strain- and
stress-like quantities) via Message Passing Interface (MPI).