Abstract:

The mechanical behavior of heterogeneus materials such as
composites, polycrystals or cellular materials, depends on their actual
microstructure. Computational homogenization is a powerful tool that
allows to link macroscopic behavior with microstructure by solving a
boundary value problem on a periodic Representative Volume Element (RVE)
of the microstructure. Fast Fourier Transform (FFT) based spectral
methods have become a very popular option in the last 15 years to solve
the periodic boundary value problem in computational homogenization. The
main advantages of FFT respect to Finite Elements (FE) based
homogenization are the very high numerical performance and the absence
of a mesh that allow simulating very detailed RVEs and the direct use of
images or tomographic data as input. In this work, a home-made FFT
computational homogenization code, FFTMAD, is developed using python.
The code includes the different resolution schemes based on the original
approach for linear problems. Non-linear problems for both small and
finite strains are also implemented in the code using a variational
approach.